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

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

Solve for x

$$x=\frac{\sqrt{301}-17}{2}\approx 0.174675786$$

$$x=\frac{-\sqrt{301}-17}{2}\approx -17.174675786$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -2 by x+6.

$$x\left(x-2x-12\right)=5x-3$$

Combine x and -2x to get -x.

$$x\left(-x-12\right)=5x-3$$

Use the distributive property to multiply x by -x-12.

$$-x^{2}-12x=5x-3$$

Subtract 5x from both sides.

$$-x^{2}-12x-5x=-3$$

Combine -12x and -5x to get -17x.

$$-x^{2}-17x=-3$$

Add 3 to both sides.

$$-x^{2}-17x+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -17 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Square -17.

$$x=\frac{-\left(-17\right)±\sqrt{289-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-17\right)±\sqrt{289+4\times 3}}{2\left(-1\right)}$$

Multiply 4 times 3.

$$x=\frac{-\left(-17\right)±\sqrt{289+12}}{2\left(-1\right)}$$

Add 289 to 12.

$$x=\frac{-\left(-17\right)±\sqrt{301}}{2\left(-1\right)}$$

The opposite of -17 is 17.

$$x=\frac{17±\sqrt{301}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{17±\sqrt{301}}{-2}$$

Now solve the equation x=\frac{17±\sqrt{301}}{-2} when ± is plus. Add 17 to \sqrt{301}.

$$x=\frac{\sqrt{301}+17}{-2}$$

Divide 17+\sqrt{301} by -2.

$$x=\frac{-\sqrt{301}-17}{2}$$

Now solve the equation x=\frac{17±\sqrt{301}}{-2} when ± is minus. Subtract \sqrt{301} from 17.

$$x=\frac{17-\sqrt{301}}{-2}$$

Divide 17-\sqrt{301} by -2.

$$x=\frac{\sqrt{301}-17}{2}$$

The equation is now solved.

$$x=\frac{-\sqrt{301}-17}{2} x=\frac{\sqrt{301}-17}{2}$$

Steps for Completing the Square

Use the distributive property to multiply -2 by x+6.

$$x\left(x-2x-12\right)=5x-3$$

Combine x and -2x to get -x.

$$x\left(-x-12\right)=5x-3$$

Use the distributive property to multiply x by -x-12.

$$-x^{2}-12x=5x-3$$

Subtract 5x from both sides.

$$-x^{2}-12x-5x=-3$$

Combine -12x and -5x to get -17x.

$$-x^{2}-17x=-3$$

Divide both sides by -1.

$$\frac{-x^{2}-17x}{-1}=-\frac{3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\left(-\frac{17}{-1}\right)x=-\frac{3}{-1}$$

Divide -17 by -1.

$$x^{2}+17x=-\frac{3}{-1}$$

Divide -3 by -1.

$$x^{2}+17x=3$$

Divide 17, the coefficient of the x term, by 2 to get \frac{17}{2}. Then add the square of \frac{17}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+17x+\left(\frac{17}{2}\right)^{2}=3+\left(\frac{17}{2}\right)^{2}$$

Square \frac{17}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+17x+\frac{289}{4}=3+\frac{289}{4}$$

Add 3 to \frac{289}{4}.

$$x^{2}+17x+\frac{289}{4}=\frac{301}{4}$$

Factor x^{2}+17x+\frac{289}{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}.

$$\left(x+\frac{17}{2}\right)^{2}=\frac{301}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{17}{2}\right)^{2}}=\sqrt{\frac{301}{4}}$$

Simplify.

$$x+\frac{17}{2}=\frac{\sqrt{301}}{2} x+\frac{17}{2}=-\frac{\sqrt{301}}{2}$$

Subtract \frac{17}{2} from both sides of the equation.

$$x=\frac{\sqrt{301}-17}{2} x=\frac{-\sqrt{301}-17}{2}$$