Solve 7x^2+43-137=0

$$7 { x }^{ 2 } +43-137=0$$

Solve for x

$$x = \frac{\sqrt{658}}{7} \approx 3.664501525$$

$$x = -\frac{\sqrt{658}}{7} \approx -3.664501525$$

Steps by Finding Square Root

Subtract 137 from 43 to get -94.

$$7x^{2}-94=0$$

Add 94 to both sides. Anything plus zero gives itself.

$$7x^{2}=94$$

Divide both sides by 7.

$$x^{2}=\frac{94}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{658}}{7} x=-\frac{\sqrt{658}}{7}$$

Steps Using the Quadratic Formula

Subtract 137 from 43 to get -94.

$$7x^{2}-94=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -94 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-94\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-94\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-94\right)}}{2\times 7}$$

Multiply -28 times -94.

$$x=\frac{0±\sqrt{2632}}{2\times 7}$$

Take the square root of 2632.

$$x=\frac{0±2\sqrt{658}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±2\sqrt{658}}{14}$$

Now solve the equation x=\frac{0±2\sqrt{658}}{14} when ± is plus.

$$x=\frac{\sqrt{658}}{7}$$

Now solve the equation x=\frac{0±2\sqrt{658}}{14} when ± is minus.

$$x=-\frac{\sqrt{658}}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{658}}{7} x=-\frac{\sqrt{658}}{7}$$