Solve 9/25+265x^2/25=1

$$\frac { 9 } { 25 } + \frac { 265 x ^ { 2 } } { 25 } = 1$$

Solve for x

$$x=\frac{4\sqrt{265}}{265}\approx 0.245718047$$

$$x=-\frac{4\sqrt{265}}{265}\approx -0.245718047$$

Steps by Finding Square Root

Multiply both sides of the equation by 25.

$$9+265x^{2}=25$$

Subtract 9 from both sides.

$$265x^{2}=25-9$$

Subtract 9 from 25 to get 16.

$$265x^{2}=16$$

Divide both sides by 265.

$$x^{2}=\frac{16}{265}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{265}}{265} x=-\frac{4\sqrt{265}}{265}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 25.

$$9+265x^{2}=25$$

Subtract 25 from both sides.

$$9+265x^{2}-25=0$$

Subtract 25 from 9 to get -16.

$$-16+265x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$265x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 265 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 265\left(-16\right)}}{2\times 265}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 265\left(-16\right)}}{2\times 265}$$

Multiply -4 times 265.

$$x=\frac{0±\sqrt{-1060\left(-16\right)}}{2\times 265}$$

Multiply -1060 times -16.

$$x=\frac{0±\sqrt{16960}}{2\times 265}$$

Take the square root of 16960.

$$x=\frac{0±8\sqrt{265}}{2\times 265}$$

Multiply 2 times 265.

$$x=\frac{0±8\sqrt{265}}{530}$$

Now solve the equation x=\frac{0±8\sqrt{265}}{530} when ± is plus.

$$x=\frac{4\sqrt{265}}{265}$$

Now solve the equation x=\frac{0±8\sqrt{265}}{530} when ± is minus.

$$x=-\frac{4\sqrt{265}}{265}$$

The equation is now solved.

$$x=\frac{4\sqrt{265}}{265} x=-\frac{4\sqrt{265}}{265}$$