Solve -793x+9left(x-15right)+4left(x-4right)x/x=0

$$-793x+9 \left( x-15 \right) +4 \left( x-4 \right) \frac{ x }{ x } =0$$

Solve for x

$$x=-\frac{151}{780}\approx -0.193589744$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Multiply x and x to get x^{2}.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9 by x-15.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9x-135 by x.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

Combine -793x^{2} and 9x^{2} to get -784x^{2}.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 4 by x-4.

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

Use the distributive property to multiply 4x-16 by x.

$$-784x^{2}-135x+4x^{2}-16x=0$$

Combine -784x^{2} and 4x^{2} to get -780x^{2}.

$$-780x^{2}-135x-16x=0$$

Combine -135x and -16x to get -151x.

$$-780x^{2}-151x=0$$

Factor out x.

$$x\left(-780x-151\right)=0$$

To find equation solutions, solve x=0 and -780x-151=0.

$$x=0 x=-\frac{151}{780}$$

Variable x cannot be equal to 0.

$$x=-\frac{151}{780}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Multiply x and x to get x^{2}.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9 by x-15.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9x-135 by x.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

Combine -793x^{2} and 9x^{2} to get -784x^{2}.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 4 by x-4.

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

Use the distributive property to multiply 4x-16 by x.

$$-784x^{2}-135x+4x^{2}-16x=0$$

Combine -784x^{2} and 4x^{2} to get -780x^{2}.

$$-780x^{2}-135x-16x=0$$

Combine -135x and -16x to get -151x.

$$-780x^{2}-151x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -780 for a, -151 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-151\right)±\sqrt{\left(-151\right)^{2}}}{2\left(-780\right)}$$

Take the square root of \left(-151\right)^{2}.

$$x=\frac{-\left(-151\right)±151}{2\left(-780\right)}$$

The opposite of -151 is 151.

$$x=\frac{151±151}{2\left(-780\right)}$$

Multiply 2 times -780.

$$x=\frac{151±151}{-1560}$$

Now solve the equation x=\frac{151±151}{-1560} when ± is plus. Add 151 to 151.

$$x=\frac{302}{-1560}$$

Reduce the fraction \frac{302}{-1560} to lowest terms by extracting and canceling out 2.

$$x=-\frac{151}{780}$$

Now solve the equation x=\frac{151±151}{-1560} when ± is minus. Subtract 151 from 151.

$$x=\frac{0}{-1560}$$

Divide 0 by -1560.

$$x=0$$

The equation is now solved.

$$x=-\frac{151}{780} x=0$$

Variable x cannot be equal to 0.

$$x=-\frac{151}{780}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Multiply x and x to get x^{2}.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9 by x-15.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9x-135 by x.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

Combine -793x^{2} and 9x^{2} to get -784x^{2}.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 4 by x-4.

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

Use the distributive property to multiply 4x-16 by x.

$$-784x^{2}-135x+4x^{2}-16x=0$$

Combine -784x^{2} and 4x^{2} to get -780x^{2}.

$$-780x^{2}-135x-16x=0$$

Combine -135x and -16x to get -151x.

$$-780x^{2}-151x=0$$

Divide both sides by -780.

$$\frac{-780x^{2}-151x}{-780}=\frac{0}{-780}$$

Dividing by -780 undoes the multiplication by -780.

$$x^{2}+\left(-\frac{151}{-780}\right)x=\frac{0}{-780}$$

Divide -151 by -780.

$$x^{2}+\frac{151}{780}x=\frac{0}{-780}$$

Divide 0 by -780.

$$x^{2}+\frac{151}{780}x=0$$

Divide \frac{151}{780}, the coefficient of the x term, by 2 to get \frac{151}{1560}. Then add the square of \frac{151}{1560} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{151}{780}x+\left(\frac{151}{1560}\right)^{2}=\left(\frac{151}{1560}\right)^{2}$$

Square \frac{151}{1560} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{151}{780}x+\frac{22801}{2433600}=\frac{22801}{2433600}$$

Factor x^{2}+\frac{151}{780}x+\frac{22801}{2433600}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{151}{1560}\right)^{2}=\frac{22801}{2433600}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{151}{1560}\right)^{2}}=\sqrt{\frac{22801}{2433600}}$$

Simplify.

$$x+\frac{151}{1560}=\frac{151}{1560} x+\frac{151}{1560}=-\frac{151}{1560}$$

Subtract \frac{151}{1560} from both sides of the equation.

$$x=0 x=-\frac{151}{780}$$

Variable x cannot be equal to 0.

$$x=-\frac{151}{780}$$