How to solve x + x - 10 = 0 1

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 x + x - 10 = 0 1 | Equatix

Question

$$( 1 ) + x ^ { 2 } + x - 10 = 0$$

Solve for x

$x = \frac{\sqrt{37} - 1}{2} \approx 2.541381265$
$x=\frac{-\sqrt{37}-1}{2}\approx -3.541381265$

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Subtract $10$ from $1$ to get $-9$.

$$-9+x^{2}+x=0$$

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.

$$x^{2}+x-9=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $1$ for $b$, and $-9$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-9\right)}}{2}$$

Square $1$.

$$x=\frac{-1±\sqrt{1-4\left(-9\right)}}{2}$$

Multiply $-4$ times $-9$.

$$x=\frac{-1±\sqrt{1+36}}{2}$$

Add $1$ to $36$.

$$x=\frac{-1±\sqrt{37}}{2}$$

Now solve the equation $x=\frac{-1±\sqrt{37}}{2}$ when $±$ is plus. Add $-1$ to $\sqrt{37}$.

$$x=\frac{\sqrt{37}-1}{2}$$

Now solve the equation $x=\frac{-1±\sqrt{37}}{2}$ when $±$ is minus. Subtract $\sqrt{37}$ from $-1$.

$$x=\frac{-\sqrt{37}-1}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{37}-1}{2}$$ $$x=\frac{-\sqrt{37}-1}{2}$$

Steps for Completing the Square

Subtract $10$ from $1$ to get $-9$.

$$-9+x^{2}+x=0$$

Add $9$ to both sides. Anything plus zero gives itself.

$$x^{2}+x=9$$

Divide $1$, the coefficient of the $x$ term, by $2$ to get $\frac{1}{2}$. Then add the square of $\frac{1}{2}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=9+\left(\frac{1}{2}\right)^{2}$$

Square $\frac{1}{2}$ by squaring both the numerator and the denominator of the fraction.

$$x^{2}+x+\frac{1}{4}=9+\frac{1}{4}$$

Add $9$ to $\frac{1}{4}$.

$$x^{2}+x+\frac{1}{4}=\frac{37}{4}$$

Factor $x^{2}+x+\frac{1}{4}$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{37}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{37}{4}}$$

Simplify.

$$x+\frac{1}{2}=\frac{\sqrt{37}}{2}$$ $$x+\frac{1}{2}=-\frac{\sqrt{37}}{2}$$

Subtract $\frac{1}{2}$ from both sides of the equation.

$$x=\frac{\sqrt{37}-1}{2}$$ $$x=\frac{-\sqrt{37}-1}{2}$$

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Solve for x

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Steps for Completing the Square