Solve 1x(56x+16)=1.52

$$1x(56x+16)=1.52$$

Solve for x

$$x=\frac{\sqrt{233}}{70}-\frac{1}{7}\approx 0.075204822$$

$$x=-\frac{\sqrt{233}}{70}-\frac{1}{7}\approx -0.360919107$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 1x by 56x+16.

$$56x^{2}+16x=1.52$$

Subtract 1.52 from both sides.

$$56x^{2}+16x-1.52=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 56 for a, 16 for b, and -1.52 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\times 56\left(-1.52\right)}}{2\times 56}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\times 56\left(-1.52\right)}}{2\times 56}$$

Multiply -4 times 56.

$$x=\frac{-16±\sqrt{256-224\left(-1.52\right)}}{2\times 56}$$

Multiply -224 times -1.52.

$$x=\frac{-16±\sqrt{256+340.48}}{2\times 56}$$

Add 256 to 340.48.

$$x=\frac{-16±\sqrt{596.48}}{2\times 56}$$

Take the square root of 596.48.

$$x=\frac{-16±\frac{8\sqrt{233}}{5}}{2\times 56}$$

Multiply 2 times 56.

$$x=\frac{-16±\frac{8\sqrt{233}}{5}}{112}$$

Now solve the equation x=\frac{-16±\frac{8\sqrt{233}}{5}}{112} when ± is plus. Add -16 to \frac{8\sqrt{233}}{5}.

$$x=\frac{\frac{8\sqrt{233}}{5}-16}{112}$$

Divide -16+\frac{8\sqrt{233}}{5} by 112.

$$x=\frac{\sqrt{233}}{70}-\frac{1}{7}$$

Now solve the equation x=\frac{-16±\frac{8\sqrt{233}}{5}}{112} when ± is minus. Subtract \frac{8\sqrt{233}}{5} from -16.

$$x=\frac{-\frac{8\sqrt{233}}{5}-16}{112}$$

Divide -16-\frac{8\sqrt{233}}{5} by 112.

$$x=-\frac{\sqrt{233}}{70}-\frac{1}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{233}}{70}-\frac{1}{7} x=-\frac{\sqrt{233}}{70}-\frac{1}{7}$$

Steps for Completing the Square

Use the distributive property to multiply 1x by 56x+16.

$$56x^{2}+16x=1.52$$

Divide both sides by 56.

$$\frac{56x^{2}+16x}{56}=\frac{1.52}{56}$$

Dividing by 56 undoes the multiplication by 56.

$$x^{2}+\frac{16}{56}x=\frac{1.52}{56}$$

Reduce the fraction \frac{16}{56} to lowest terms by extracting and canceling out 8.

$$x^{2}+\frac{2}{7}x=\frac{1.52}{56}$$

Divide 1.52 by 56.

$$x^{2}+\frac{2}{7}x=\frac{19}{700}$$

Divide \frac{2}{7}, the coefficient of the x term, by 2 to get \frac{1}{7}. Then add the square of \frac{1}{7} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{2}{7}x+\left(\frac{1}{7}\right)^{2}=\frac{19}{700}+\left(\frac{1}{7}\right)^{2}$$

Square \frac{1}{7} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{2}{7}x+\frac{1}{49}=\frac{19}{700}+\frac{1}{49}$$

Add \frac{19}{700} to \frac{1}{49} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{2}{7}x+\frac{1}{49}=\frac{233}{4900}$$

Factor x^{2}+\frac{2}{7}x+\frac{1}{49}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{7}\right)^{2}=\frac{233}{4900}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{7}\right)^{2}}=\sqrt{\frac{233}{4900}}$$

Simplify.

$$x+\frac{1}{7}=\frac{\sqrt{233}}{70} x+\frac{1}{7}=-\frac{\sqrt{233}}{70}$$

Subtract \frac{1}{7} from both sides of the equation.

$$x=\frac{\sqrt{233}}{70}-\frac{1}{7} x=-\frac{\sqrt{233}}{70}-\frac{1}{7}$$