Solve x-4[x*2(x+6)]=5x+3

$$x - 4 [ x \cdot 2 ( x + 6 ) ] = 5 x + 3$$

Solve for x

$$x=\frac{\sqrt{163}-13}{4}\approx -0.058213666$$

$$x=\frac{-\sqrt{163}-13}{4}\approx -6.441786334$$

Steps Using the Quadratic Formula

Multiply 4 and 2 to get 8.

$$x-8x\left(x+6\right)=5x+3$$

Subtract 5x from both sides.

$$x-8x\left(x+6\right)-5x=3$$

Subtract 3 from both sides.

$$x-8x\left(x+6\right)-5x-3=0$$

Use the distributive property to multiply -8x by x+6.

$$x-8x^{2}-48x-5x-3=0$$

Combine x and -48x to get -47x.

$$-47x-8x^{2}-5x-3=0$$

Combine -47x and -5x to get -52x.

$$-52x-8x^{2}-3=0$$

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.

$$-8x^{2}-52x-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -8 for a, -52 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-52\right)±\sqrt{\left(-52\right)^{2}-4\left(-8\right)\left(-3\right)}}{2\left(-8\right)}$$

Square -52.

$$x=\frac{-\left(-52\right)±\sqrt{2704-4\left(-8\right)\left(-3\right)}}{2\left(-8\right)}$$

Multiply -4 times -8.

$$x=\frac{-\left(-52\right)±\sqrt{2704+32\left(-3\right)}}{2\left(-8\right)}$$

Multiply 32 times -3.

$$x=\frac{-\left(-52\right)±\sqrt{2704-96}}{2\left(-8\right)}$$

Add 2704 to -96.

$$x=\frac{-\left(-52\right)±\sqrt{2608}}{2\left(-8\right)}$$

Take the square root of 2608.

$$x=\frac{-\left(-52\right)±4\sqrt{163}}{2\left(-8\right)}$$

The opposite of -52 is 52.

$$x=\frac{52±4\sqrt{163}}{2\left(-8\right)}$$

Multiply 2 times -8.

$$x=\frac{52±4\sqrt{163}}{-16}$$

Now solve the equation x=\frac{52±4\sqrt{163}}{-16} when ± is plus. Add 52 to 4\sqrt{163}.

$$x=\frac{4\sqrt{163}+52}{-16}$$

Divide 52+4\sqrt{163} by -16.

$$x=\frac{-\sqrt{163}-13}{4}$$

Now solve the equation x=\frac{52±4\sqrt{163}}{-16} when ± is minus. Subtract 4\sqrt{163} from 52.

$$x=\frac{52-4\sqrt{163}}{-16}$$

Divide 52-4\sqrt{163} by -16.

$$x=\frac{\sqrt{163}-13}{4}$$

The equation is now solved.

$$x=\frac{-\sqrt{163}-13}{4} x=\frac{\sqrt{163}-13}{4}$$

Steps for Completing the Square

Multiply 4 and 2 to get 8.

$$x-8x\left(x+6\right)=5x+3$$

Subtract 5x from both sides.

$$x-8x\left(x+6\right)-5x=3$$

Use the distributive property to multiply -8x by x+6.

$$x-8x^{2}-48x-5x=3$$

Combine x and -48x to get -47x.

$$-47x-8x^{2}-5x=3$$

Combine -47x and -5x to get -52x.

$$-52x-8x^{2}=3$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-8x^{2}-52x=3$$

Divide both sides by -8.

$$\frac{-8x^{2}-52x}{-8}=\frac{3}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x^{2}+\left(-\frac{52}{-8}\right)x=\frac{3}{-8}$$

Reduce the fraction \frac{-52}{-8} to lowest terms by extracting and canceling out 4.

$$x^{2}+\frac{13}{2}x=\frac{3}{-8}$$

Divide 3 by -8.

$$x^{2}+\frac{13}{2}x=-\frac{3}{8}$$

Divide \frac{13}{2}, the coefficient of the x term, by 2 to get \frac{13}{4}. Then add the square of \frac{13}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{13}{2}x+\left(\frac{13}{4}\right)^{2}=-\frac{3}{8}+\left(\frac{13}{4}\right)^{2}$$

Square \frac{13}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{13}{2}x+\frac{169}{16}=-\frac{3}{8}+\frac{169}{16}$$

Add -\frac{3}{8} to \frac{169}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{13}{2}x+\frac{169}{16}=\frac{163}{16}$$

Factor x^{2}+\frac{13}{2}x+\frac{169}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{13}{4}\right)^{2}=\frac{163}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{13}{4}\right)^{2}}=\sqrt{\frac{163}{16}}$$

Simplify.

$$x+\frac{13}{4}=\frac{\sqrt{163}}{4} x+\frac{13}{4}=-\frac{\sqrt{163}}{4}$$

Subtract \frac{13}{4} from both sides of the equation.

$$x=\frac{\sqrt{163}-13}{4} x=\frac{-\sqrt{163}-13}{4}$$