Solve -49/8=x(2x-7)

$$- \frac{ 49 }{ 8 } =x(2x-7)$$

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by 2x-7.

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

Swap sides so that all variable terms are on the left hand side.

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

Add \frac{49}{8} to both sides.

$$2x^{2}-7x+\frac{49}{8}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -7 for b, and \frac{49}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 2\times \frac{49}{8}}}{2\times 2}$$

Square -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 2\times \frac{49}{8}}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-7\right)±\sqrt{49-8\times \frac{49}{8}}}{2\times 2}$$

Multiply -8 times \frac{49}{8}.

$$x=\frac{-\left(-7\right)±\sqrt{49-49}}{2\times 2}$$

Add 49 to -49.

$$x=\frac{-\left(-7\right)±\sqrt{0}}{2\times 2}$$

Take the square root of 0.

$$x=-\frac{-7}{2\times 2}$$

The opposite of -7 is 7.

$$x=\frac{7}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{7}{4}$$

Steps for Completing the Square

Use the distributive property to multiply x by 2x-7.

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

Swap sides so that all variable terms are on the left hand side.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide -\frac{49}{8} by 2.

$$x^{2}-\frac{7}{2}x=-\frac{49}{16}$$

Divide -\frac{7}{2}, the coefficient of the x term, by 2 to get -\frac{7}{4}. Then add the square of -\frac{7}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{2}x+\left(-\frac{7}{4}\right)^{2}=-\frac{49}{16}+\left(-\frac{7}{4}\right)^{2}$$

Square -\frac{7}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=\frac{-49+49}{16}$$

Add -\frac{49}{16} to \frac{49}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=0$$

Factor x^{2}-\frac{7}{2}x+\frac{49}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{4}\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{4}\right)^{2}}=\sqrt{0}$$

Simplify.

$$x-\frac{7}{4}=0 x-\frac{7}{4}=0$$

Add \frac{7}{4} to both sides of the equation.

$$x=\frac{7}{4} x=\frac{7}{4}$$

The equation is now solved. Solutions are the same.

$$x=\frac{7}{4}$$