How to solve 1.8x+0.7/x=0.94

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 1.8x+0.7/x=0.94 | Equatix

Question

$$1.8x+0.7/x=0.94$$

Solve for x (complex solution)

$x=\frac{47+i\sqrt{10391}}{180}\approx 0.261111111+0.566312526i$
$x=\frac{-i\sqrt{10391}+47}{180}\approx 0.261111111-0.566312526i$

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.

$$1.8xx+0.7=0.94x$$

Multiply $x$ and $x$ to get $x^{2}$.

$$1.8x^{2}+0.7=0.94x$$

Subtract $0.94x$ from both sides.

$$1.8x^{2}+0.7-0.94x=0$$

All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.

$$1.8x^{2}-0.94x+0.7=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1.8$ for $a$, $-0.94$ for $b$, and $0.7$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-\left(-0.94\right)±\sqrt{\left(-0.94\right)^{2}-4\times 1.8\times 0.7}}{2\times 1.8}$$

Square $-0.94$ by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-0.94\right)±\sqrt{0.8836-4\times 1.8\times 0.7}}{2\times 1.8}$$

Multiply $-4$ times $1.8$.

$$x=\frac{-\left(-0.94\right)±\sqrt{0.8836-7.2\times 0.7}}{2\times 1.8}$$

Multiply $-7.2$ times $0.7$ by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-0.94\right)±\sqrt{0.8836-5.04}}{2\times 1.8}$$

Add $0.8836$ to $-5.04$ by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-0.94\right)±\sqrt{-4.1564}}{2\times 1.8}$$

Take the square root of $-4.1564$.

$$x=\frac{-\left(-0.94\right)±\frac{\sqrt{10391}i}{50}}{2\times 1.8}$$

The opposite of $-0.94$ is $0.94$.

$$x=\frac{0.94±\frac{\sqrt{10391}i}{50}}{2\times 1.8}$$

Multiply $2$ times $1.8$.

$$x=\frac{0.94±\frac{\sqrt{10391}i}{50}}{3.6}$$

Now solve the equation $x=\frac{0.94±\frac{\sqrt{10391}i}{50}}{3.6}$ when $±$ is plus. Add $0.94$ to $\frac{i\sqrt{10391}}{50}$.

$$x=\frac{47+\sqrt{10391}i}{3.6\times 50}$$

Divide $\frac{47+i\sqrt{10391}}{50}$ by $3.6$ by multiplying $\frac{47+i\sqrt{10391}}{50}$ by the reciprocal of $3.6$.

$$x=\frac{47+\sqrt{10391}i}{180}$$

Now solve the equation $x=\frac{0.94±\frac{\sqrt{10391}i}{50}}{3.6}$ when $±$ is minus. Subtract $\frac{i\sqrt{10391}}{50}$ from $0.94$.

$$x=\frac{-\sqrt{10391}i+47}{3.6\times 50}$$

Divide $\frac{47-i\sqrt{10391}}{50}$ by $3.6$ by multiplying $\frac{47-i\sqrt{10391}}{50}$ by the reciprocal of $3.6$.

$$x=\frac{-\sqrt{10391}i+47}{180}$$

The equation is now solved.

$$x=\frac{47+\sqrt{10391}i}{180}$$ $$x=\frac{-\sqrt{10391}i+47}{180}$$

Steps for Completing the Square

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.

$$1.8xx+0.7=0.94x$$

Multiply $x$ and $x$ to get $x^{2}$.

$$1.8x^{2}+0.7=0.94x$$

Subtract $0.94x$ from both sides.

$$1.8x^{2}+0.7-0.94x=0$$

Subtract $0.7$ from both sides. Anything subtracted from zero gives its negation.

$$1.8x^{2}-0.94x=-0.7$$

Divide both sides of the equation by $1.8$, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{1.8x^{2}-0.94x}{1.8}=-\frac{0.7}{1.8}$$

Dividing by $1.8$ undoes the multiplication by $1.8$.

$$x^{2}+\left(-\frac{0.94}{1.8}\right)x=-\frac{0.7}{1.8}$$

Divide $-0.94$ by $1.8$ by multiplying $-0.94$ by the reciprocal of $1.8$.

$$x^{2}-\frac{47}{90}x=-\frac{0.7}{1.8}$$

Divide $-0.7$ by $1.8$ by multiplying $-0.7$ by the reciprocal of $1.8$.

$$x^{2}-\frac{47}{90}x=-\frac{7}{18}$$

Divide $-\frac{47}{90}$, the coefficient of the $x$ term, by $2$ to get $-\frac{47}{180}$. Then add the square of $-\frac{47}{180}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{47}{90}x+\left(-\frac{47}{180}\right)^{2}=-\frac{7}{18}+\left(-\frac{47}{180}\right)^{2}$$

Square $-\frac{47}{180}$ by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{47}{90}x+\frac{2209}{32400}=-\frac{7}{18}+\frac{2209}{32400}$$

Add $-\frac{7}{18}$ to $\frac{2209}{32400}$ by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{47}{90}x+\frac{2209}{32400}=-\frac{10391}{32400}$$

Factor $x^{2}-\frac{47}{90}x+\frac{2209}{32400}$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x-\frac{47}{180}\right)^{2}=-\frac{10391}{32400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{47}{180}\right)^{2}}=\sqrt{-\frac{10391}{32400}}$$

Simplify.

$$x-\frac{47}{180}=\frac{\sqrt{10391}i}{180}$$ $$x-\frac{47}{180}=-\frac{\sqrt{10391}i}{180}$$

Add $\frac{47}{180}$ to both sides of the equation.

$$x=\frac{47+\sqrt{10391}i}{180}$$ $$x=\frac{-\sqrt{10391}i+47}{180}$$

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Example

Question

Solve for x (complex solution)

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Steps for Completing the Square