Solve -7.93x+9left(x-1.5right)+4left(x-4right)x/x=0

$$-7.93x+9 \left( x-1.5 \right) +4 \left( x-4 \right) \frac{ x }{ x } =0$$

Solve for x

$$x = \frac{2950}{507} = 5\frac{415}{507} \approx 5.818540434$$

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.

$$-7.93xx+9\left(x-1.5\right)x+4\left(x-4\right)x=0$$

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

$$-7.93x^{2}+9\left(x-1.5\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9 by x-1.5.

$$-7.93x^{2}+\left(9x-13.5\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9x-13.5 by x.

$$-7.93x^{2}+9x^{2}-13.5x+4\left(x-4\right)x=0$$

Combine -7.93x^{2} and 9x^{2} to get 1.07x^{2}.

$$1.07x^{2}-13.5x+4\left(x-4\right)x=0$$

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

$$1.07x^{2}-13.5x+\left(4x-16\right)x=0$$

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

$$1.07x^{2}-13.5x+4x^{2}-16x=0$$

Combine 1.07x^{2} and 4x^{2} to get 5.07x^{2}.

$$5.07x^{2}-13.5x-16x=0$$

Combine -13.5x and -16x to get -29.5x.

$$5.07x^{2}-29.5x=0$$

Factor out x.

$$x\left(5.07x-29.5\right)=0$$

To find equation solutions, solve x=0 and \frac{507x}{100}-29.5=0.

$$x=0 x=\frac{2950}{507}$$

Variable x cannot be equal to 0.

$$x=\frac{2950}{507}$$

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.

$$-7.93xx+9\left(x-1.5\right)x+4\left(x-4\right)x=0$$

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

$$-7.93x^{2}+9\left(x-1.5\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9 by x-1.5.

$$-7.93x^{2}+\left(9x-13.5\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9x-13.5 by x.

$$-7.93x^{2}+9x^{2}-13.5x+4\left(x-4\right)x=0$$

Combine -7.93x^{2} and 9x^{2} to get 1.07x^{2}.

$$1.07x^{2}-13.5x+4\left(x-4\right)x=0$$

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

$$1.07x^{2}-13.5x+\left(4x-16\right)x=0$$

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

$$1.07x^{2}-13.5x+4x^{2}-16x=0$$

Combine 1.07x^{2} and 4x^{2} to get 5.07x^{2}.

$$5.07x^{2}-13.5x-16x=0$$

Combine -13.5x and -16x to get -29.5x.

$$5.07x^{2}-29.5x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5.07 for a, -29.5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-29.5\right)±\sqrt{\left(-29.5\right)^{2}}}{2\times 5.07}$$

Take the square root of \left(-29.5\right)^{2}.

$$x=\frac{-\left(-29.5\right)±\frac{59}{2}}{2\times 5.07}$$

The opposite of -29.5 is 29.5.

$$x=\frac{29.5±\frac{59}{2}}{2\times 5.07}$$

Multiply 2 times 5.07.

$$x=\frac{29.5±\frac{59}{2}}{10.14}$$

Now solve the equation x=\frac{29.5±\frac{59}{2}}{10.14} when ± is plus. Add 29.5 to \frac{59}{2} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{59}{10.14}$$

Divide 59 by 10.14 by multiplying 59 by the reciprocal of 10.14.

$$x=\frac{2950}{507}$$

Now solve the equation x=\frac{29.5±\frac{59}{2}}{10.14} when ± is minus. Subtract \frac{59}{2} from 29.5 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{10.14}$$

Divide 0 by 10.14 by multiplying 0 by the reciprocal of 10.14.

$$x=0$$

The equation is now solved.

$$x=\frac{2950}{507} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{2950}{507}$$

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.

$$-7.93xx+9\left(x-1.5\right)x+4\left(x-4\right)x=0$$

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

$$-7.93x^{2}+9\left(x-1.5\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9 by x-1.5.

$$-7.93x^{2}+\left(9x-13.5\right)x+4\left(x-4\right)x=0$$

Use the distributive property to multiply 9x-13.5 by x.

$$-7.93x^{2}+9x^{2}-13.5x+4\left(x-4\right)x=0$$

Combine -7.93x^{2} and 9x^{2} to get 1.07x^{2}.

$$1.07x^{2}-13.5x+4\left(x-4\right)x=0$$

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

$$1.07x^{2}-13.5x+\left(4x-16\right)x=0$$

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

$$1.07x^{2}-13.5x+4x^{2}-16x=0$$

Combine 1.07x^{2} and 4x^{2} to get 5.07x^{2}.

$$5.07x^{2}-13.5x-16x=0$$

Combine -13.5x and -16x to get -29.5x.

$$5.07x^{2}-29.5x=0$$

Divide both sides of the equation by 5.07, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{5.07x^{2}-29.5x}{5.07}=\frac{0}{5.07}$$

Dividing by 5.07 undoes the multiplication by 5.07.

$$x^{2}+\left(-\frac{29.5}{5.07}\right)x=\frac{0}{5.07}$$

Divide -29.5 by 5.07 by multiplying -29.5 by the reciprocal of 5.07.

$$x^{2}-\frac{2950}{507}x=\frac{0}{5.07}$$

Divide 0 by 5.07 by multiplying 0 by the reciprocal of 5.07.

$$x^{2}-\frac{2950}{507}x=0$$

Divide -\frac{2950}{507}, the coefficient of the x term, by 2 to get -\frac{1475}{507}. Then add the square of -\frac{1475}{507} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{2950}{507}x+\left(-\frac{1475}{507}\right)^{2}=\left(-\frac{1475}{507}\right)^{2}$$

Square -\frac{1475}{507} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{2950}{507}x+\frac{2175625}{257049}=\frac{2175625}{257049}$$

Factor x^{2}-\frac{2950}{507}x+\frac{2175625}{257049}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1475}{507}\right)^{2}=\frac{2175625}{257049}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1475}{507}\right)^{2}}=\sqrt{\frac{2175625}{257049}}$$

Simplify.

$$x-\frac{1475}{507}=\frac{1475}{507} x-\frac{1475}{507}=-\frac{1475}{507}$$

Add \frac{1475}{507} to both sides of the equation.

$$x=\frac{2950}{507} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{2950}{507}$$