Solve 4x*2x=7x

$$4x \times 2x=7x$$

Solve for x

$$x=\frac{7}{8}=0.875$$

$$x=0$$

Steps Using Factoring

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

$$4x^{2}\times 2=7x$$

Multiply 4 and 2 to get 8.

$$8x^{2}=7x$$

Subtract 7x from both sides.

$$8x^{2}-7x=0$$

Factor out x.

$$x\left(8x-7\right)=0$$

To find equation solutions, solve x=0 and 8x-7=0.

$$x=0 x=\frac{7}{8}$$

Steps Using the Quadratic Formula

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

$$4x^{2}\times 2=7x$$

Multiply 4 and 2 to get 8.

$$8x^{2}=7x$$

Subtract 7x from both sides.

$$8x^{2}-7x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, -7 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 8}$$

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

$$x=\frac{-\left(-7\right)±7}{2\times 8}$$

The opposite of -7 is 7.

$$x=\frac{7±7}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{7±7}{16}$$

Now solve the equation x=\frac{7±7}{16} when ± is plus. Add 7 to 7.

$$x=\frac{14}{16}$$

Reduce the fraction \frac{14}{16} to lowest terms by extracting and canceling out 2.

$$x=\frac{7}{8}$$

Now solve the equation x=\frac{7±7}{16} when ± is minus. Subtract 7 from 7.

$$x=\frac{0}{16}$$

Divide 0 by 16.

$$x=0$$

The equation is now solved.

$$x=\frac{7}{8} x=0$$

Steps for Completing the Square

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

$$4x^{2}\times 2=7x$$

Multiply 4 and 2 to get 8.

$$8x^{2}=7x$$

Subtract 7x from both sides.

$$8x^{2}-7x=0$$

Divide both sides by 8.

$$\frac{8x^{2}-7x}{8}=\frac{0}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x^{2}-\frac{7}{8}x=\frac{0}{8}$$

Divide 0 by 8.

$$x^{2}-\frac{7}{8}x=0$$

Divide -\frac{7}{8}, the coefficient of the x term, by 2 to get -\frac{7}{16}. Then add the square of -\frac{7}{16} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{8}x+\left(-\frac{7}{16}\right)^{2}=\left(-\frac{7}{16}\right)^{2}$$

Square -\frac{7}{16} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{8}x+\frac{49}{256}=\frac{49}{256}$$

Factor x^{2}-\frac{7}{8}x+\frac{49}{256}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{16}\right)^{2}=\frac{49}{256}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{16}\right)^{2}}=\sqrt{\frac{49}{256}}$$

Simplify.

$$x-\frac{7}{16}=\frac{7}{16} x-\frac{7}{16}=-\frac{7}{16}$$

Add \frac{7}{16} to both sides of the equation.

$$x=\frac{7}{8} x=0$$