Solve (x - 2)(x - 6) = (2x + 1)(x + 1) | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

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Question

$$(x-2)(x-6)=(2x+1)(x+1)$$

Solve for x

$x=\frac{\sqrt{165}-11}{2}\approx 0.922616289$
$x=\frac{-\sqrt{165}-11}{2}\approx -11.922616289$

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Use the distributive property to multiply $x-2$ by $x-6$ and combine like terms.

$$x^{2}-8x+12=\left(2x+1\right)\left(x+1\right)$$

Use the distributive property to multiply $2x+1$ by $x+1$ and combine like terms.

$$x^{2}-8x+12=2x^{2}+3x+1$$

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

$$x^{2}-8x+12-2x^{2}=3x+1$$

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

$$-x^{2}-8x+12=3x+1$$

Subtract $3x$ from both sides.

$$-x^{2}-8x+12-3x=1$$

Combine $-8x$ and $-3x$ to get $-11x$.

$$-x^{2}-11x+12=1$$

Subtract $1$ from both sides.

$$-x^{2}-11x+12-1=0$$

Subtract $1$ from $12$ to get $11$.

$$-x^{2}-11x+11=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-1$ for $a$, $-11$ for $b$, and $11$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\left(-1\right)\times 11}}{2\left(-1\right)}$$

Square $-11$.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\left(-1\right)\times 11}}{2\left(-1\right)}$$

Multiply $-4$ times $-1$.

$$x=\frac{-\left(-11\right)±\sqrt{121+4\times 11}}{2\left(-1\right)}$$

Multiply $4$ times $11$.

$$x=\frac{-\left(-11\right)±\sqrt{121+44}}{2\left(-1\right)}$$

Add $121$ to $44$.

$$x=\frac{-\left(-11\right)±\sqrt{165}}{2\left(-1\right)}$$

The opposite of $-11$ is $11$.

$$x=\frac{11±\sqrt{165}}{2\left(-1\right)}$$

Multiply $2$ times $-1$.

$$x=\frac{11±\sqrt{165}}{-2}$$

Now solve the equation $x=\frac{11±\sqrt{165}}{-2}$ when $±$ is plus. Add $11$ to $\sqrt{165}$.

$$x=\frac{\sqrt{165}+11}{-2}$$

Divide $11+\sqrt{165}$ by $-2$.

$$x=\frac{-\sqrt{165}-11}{2}$$

Now solve the equation $x=\frac{11±\sqrt{165}}{-2}$ when $±$ is minus. Subtract $\sqrt{165}$ from $11$.

$$x=\frac{11-\sqrt{165}}{-2}$$

Divide $11-\sqrt{165}$ by $-2$.

$$x=\frac{\sqrt{165}-11}{2}$$

The equation is now solved.

$$x=\frac{-\sqrt{165}-11}{2}$$ $$x=\frac{\sqrt{165}-11}{2}$$

Steps for Completing the Square

Use the distributive property to multiply $x-2$ by $x-6$ and combine like terms.

$$x^{2}-8x+12=\left(2x+1\right)\left(x+1\right)$$

Use the distributive property to multiply $2x+1$ by $x+1$ and combine like terms.

$$x^{2}-8x+12=2x^{2}+3x+1$$

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

$$x^{2}-8x+12-2x^{2}=3x+1$$

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

$$-x^{2}-8x+12=3x+1$$

Subtract $3x$ from both sides.

$$-x^{2}-8x+12-3x=1$$

Combine $-8x$ and $-3x$ to get $-11x$.

$$-x^{2}-11x+12=1$$

Subtract $12$ from both sides.

$$-x^{2}-11x=1-12$$

Subtract $12$ from $1$ to get $-11$.

$$-x^{2}-11x=-11$$

Divide both sides by $-1$.

$$\frac{-x^{2}-11x}{-1}=-\frac{11}{-1}$$

Dividing by $-1$ undoes the multiplication by $-1$.

$$x^{2}+\left(-\frac{11}{-1}\right)x=-\frac{11}{-1}$$

Divide $-11$ by $-1$.

$$x^{2}+11x=-\frac{11}{-1}$$

Divide $-11$ by $-1$.

$$x^{2}+11x=11$$

Divide $11$, the coefficient of the $x$ term, by $2$ to get $\frac{11}{2}$. Then add the square of $\frac{11}{2}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+11x+\left(\frac{11}{2}\right)^{2}=11+\left(\frac{11}{2}\right)^{2}$$

Square $\frac{11}{2}$ by squaring both the numerator and the denominator of the fraction.

$$x^{2}+11x+\frac{121}{4}=11+\frac{121}{4}$$

Add $11$ to $\frac{121}{4}$.

$$x^{2}+11x+\frac{121}{4}=\frac{165}{4}$$

Factor $x^{2}+11x+\frac{121}{4}$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x+\frac{11}{2}\right)^{2}=\frac{165}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{11}{2}\right)^{2}}=\sqrt{\frac{165}{4}}$$

Simplify.

$$x+\frac{11}{2}=\frac{\sqrt{165}}{2}$$ $$x+\frac{11}{2}=-\frac{\sqrt{165}}{2}$$

Subtract $\frac{11}{2}$ from both sides of the equation.

$$x=\frac{\sqrt{165}-11}{2}$$ $$x=\frac{-\sqrt{165}-11}{2}$$