Solve -29(x)^(2)-8x=8(x)^(2)-29x | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$-29 { x }^{ 2 } -8x=8 { x }^{ 2 } -29x$$

Solve for x

$x=\frac{21}{37}\approx 0.567567568$
$x=0$

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using Factoring

Subtract $8x^{2}$ from both sides.

$$-29x^{2}-8x-8x^{2}=-29x$$

Combine $-29x^{2}$ and $-8x^{2}$ to get $-37x^{2}$.

$$-37x^{2}-8x=-29x$$

Add $29x$ to both sides.

$$-37x^{2}-8x+29x=0$$

Combine $-8x$ and $29x$ to get $21x$.

$$-37x^{2}+21x=0$$

Factor out $x$.

$$x\left(-37x+21\right)=0$$

To find equation solutions, solve $x=0$ and $-37x+21=0$.

$$x=0$$ $$x=\frac{21}{37}$$

Steps Using the Quadratic Formula

Subtract $8x^{2}$ from both sides.

$$-29x^{2}-8x-8x^{2}=-29x$$

Combine $-29x^{2}$ and $-8x^{2}$ to get $-37x^{2}$.

$$-37x^{2}-8x=-29x$$

Add $29x$ to both sides.

$$-37x^{2}-8x+29x=0$$

Combine $-8x$ and $29x$ to get $21x$.

$$-37x^{2}+21x=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-37$ for $a$, $21$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-21±\sqrt{21^{2}}}{2\left(-37\right)}$$

Take the square root of $21^{2}$.

$$x=\frac{-21±21}{2\left(-37\right)}$$

Multiply $2$ times $-37$.

$$x=\frac{-21±21}{-74}$$

Now solve the equation $x=\frac{-21±21}{-74}$ when $±$ is plus. Add $-21$ to $21$.

$$x=\frac{0}{-74}$$

Divide $0$ by $-74$.

$$x=0$$

Now solve the equation $x=\frac{-21±21}{-74}$ when $±$ is minus. Subtract $21$ from $-21$.

$$x=-\frac{42}{-74}$$

Reduce the fraction $\frac{-42}{-74}$ to lowest terms by extracting and canceling out $2$.

$$x=\frac{21}{37}$$

The equation is now solved.

$$x=0$$ $$x=\frac{21}{37}$$

Steps for Completing the Square

Subtract $8x^{2}$ from both sides.

$$-29x^{2}-8x-8x^{2}=-29x$$

Combine $-29x^{2}$ and $-8x^{2}$ to get $-37x^{2}$.

$$-37x^{2}-8x=-29x$$

Add $29x$ to both sides.

$$-37x^{2}-8x+29x=0$$

Combine $-8x$ and $29x$ to get $21x$.

$$-37x^{2}+21x=0$$

Divide both sides by $-37$.

$$\frac{-37x^{2}+21x}{-37}=\frac{0}{-37}$$

Dividing by $-37$ undoes the multiplication by $-37$.

$$x^{2}+\frac{21}{-37}x=\frac{0}{-37}$$

Divide $21$ by $-37$.

$$x^{2}-\frac{21}{37}x=\frac{0}{-37}$$

Divide $0$ by $-37$.

$$x^{2}-\frac{21}{37}x=0$$

Divide $-\frac{21}{37}$, the coefficient of the $x$ term, by $2$ to get $-\frac{21}{74}$. Then add the square of $-\frac{21}{74}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{21}{37}x+\left(-\frac{21}{74}\right)^{2}=\left(-\frac{21}{74}\right)^{2}$$

Square $-\frac{21}{74}$ by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{21}{37}x+\frac{441}{5476}=\frac{441}{5476}$$

Factor $x^{2}-\frac{21}{37}x+\frac{441}{5476}$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x-\frac{21}{74}\right)^{2}=\frac{441}{5476}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{21}{74}\right)^{2}}=\sqrt{\frac{441}{5476}}$$

Simplify.

$$x-\frac{21}{74}=\frac{21}{74}$$ $$x-\frac{21}{74}=-\frac{21}{74}$$

Add $\frac{21}{74}$ to both sides of the equation.

$$x=\frac{21}{37}$$ $$x=0$$