Solve 10x^2+37-80=0

$$10 { x }^{ 2 } +37-80 = 0$$

Solve for x

$$x = \frac{\sqrt{430}}{10} \approx 2.073644135$$

$$x = -\frac{\sqrt{430}}{10} \approx -2.073644135$$

Steps by Finding Square Root

Subtract 80 from 37 to get -43.

$$10x^{2}-43=0$$

Add 43 to both sides. Anything plus zero gives itself.

$$10x^{2}=43$$

Divide both sides by 10.

$$x^{2}=\frac{43}{10}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{430}}{10} x=-\frac{\sqrt{430}}{10}$$

Steps Using the Quadratic Formula

Subtract 80 from 37 to get -43.

$$10x^{2}-43=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -43 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-43\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-43\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-43\right)}}{2\times 10}$$

Multiply -40 times -43.

$$x=\frac{0±\sqrt{1720}}{2\times 10}$$

Take the square root of 1720.

$$x=\frac{0±2\sqrt{430}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±2\sqrt{430}}{20}$$

Now solve the equation x=\frac{0±2\sqrt{430}}{20} when ± is plus.

$$x=\frac{\sqrt{430}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{430}}{20} when ± is minus.

$$x=-\frac{\sqrt{430}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{430}}{10} x=-\frac{\sqrt{430}}{10}$$