Solve 9x*(x*1)=5x+2x=

$$9x \times (x \times 1)=5x+2x=$$

Solve for x

$$x=\frac{7}{9}\approx 0.777777778$$

$$x=0$$

Steps Using Factoring

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

$$9x^{2}\times 1=5x+2x$$

Multiply 9 and 1 to get 9.

$$9x^{2}=5x+2x$$

Combine 5x and 2x to get 7x.

$$9x^{2}=7x$$

Subtract 7x from both sides.

$$9x^{2}-7x=0$$

Factor out x.

$$x\left(9x-7\right)=0$$

To find equation solutions, solve x=0 and 9x-7=0.

$$x=0 x=\frac{7}{9}$$

Steps Using the Quadratic Formula

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

$$9x^{2}\times 1=5x+2x$$

Multiply 9 and 1 to get 9.

$$9x^{2}=5x+2x$$

Combine 5x and 2x to get 7x.

$$9x^{2}=7x$$

Subtract 7x from both sides.

$$9x^{2}-7x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, -7 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 9}$$

Take the square root of \left(-7\right)^{2}.

$$x=\frac{-\left(-7\right)±7}{2\times 9}$$

The opposite of -7 is 7.

$$x=\frac{7±7}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{7±7}{18}$$

Now solve the equation x=\frac{7±7}{18} when ± is plus. Add 7 to 7.

$$x=\frac{14}{18}$$

Reduce the fraction \frac{14}{18} to lowest terms by extracting and canceling out 2.

$$x=\frac{7}{9}$$

Now solve the equation x=\frac{7±7}{18} when ± is minus. Subtract 7 from 7.

$$x=\frac{0}{18}$$

Divide 0 by 18.

$$x=0$$

The equation is now solved.

$$x=\frac{7}{9} x=0$$

Steps for Completing the Square

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

$$9x^{2}\times 1=5x+2x$$

Multiply 9 and 1 to get 9.

$$9x^{2}=5x+2x$$

Combine 5x and 2x to get 7x.

$$9x^{2}=7x$$

Subtract 7x from both sides.

$$9x^{2}-7x=0$$

Divide both sides by 9.

$$\frac{9x^{2}-7x}{9}=\frac{0}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x^{2}-\frac{7}{9}x=\frac{0}{9}$$

Divide 0 by 9.

$$x^{2}-\frac{7}{9}x=0$$

Divide -\frac{7}{9}, the coefficient of the x term, by 2 to get -\frac{7}{18}. Then add the square of -\frac{7}{18} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{9}x+\left(-\frac{7}{18}\right)^{2}=\left(-\frac{7}{18}\right)^{2}$$

Square -\frac{7}{18} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{9}x+\frac{49}{324}=\frac{49}{324}$$

Factor x^{2}-\frac{7}{9}x+\frac{49}{324}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{18}\right)^{2}=\frac{49}{324}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{18}\right)^{2}}=\sqrt{\frac{49}{324}}$$

Simplify.

$$x-\frac{7}{18}=\frac{7}{18} x-\frac{7}{18}=-\frac{7}{18}$$

Add \frac{7}{18} to both sides of the equation.

$$x=\frac{7}{9} x=0$$