Solve x^2+400=140*35

$$x ^ { 2 } + 400 = 140 \times 35$$

Solve for x

$$x=30\sqrt{5}\approx 67.082039325$$

$$x=-30\sqrt{5}\approx -67.082039325$$

Steps by Finding Square Root

Multiply 140 and 35 to get 4900.

$$x^{2}+400=4900$$

Subtract 400 from both sides.

$$x^{2}=4900-400$$

Subtract 400 from 4900 to get 4500.

$$x^{2}=4500$$

Take the square root of both sides of the equation.

$$x=30\sqrt{5} x=-30\sqrt{5}$$

Steps Using the Quadratic Formula

Multiply 140 and 35 to get 4900.

$$x^{2}+400=4900$$

Subtract 4900 from both sides.

$$x^{2}+400-4900=0$$

Subtract 4900 from 400 to get -4500.

$$x^{2}-4500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4500\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4500\right)}}{2}$$

Multiply -4 times -4500.

$$x=\frac{0±\sqrt{18000}}{2}$$

Take the square root of 18000.

$$x=\frac{0±60\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±60\sqrt{5}}{2} when ± is plus.

$$x=30\sqrt{5}$$

Now solve the equation x=\frac{0±60\sqrt{5}}{2} when ± is minus.

$$x=-30\sqrt{5}$$

The equation is now solved.

$$x=30\sqrt{5} x=-30\sqrt{5}$$