Solve 1/2=64x^2+25x^2-19/120x^2

$$\frac { 1 } { 2 } = \frac { 64 x ^ { 2 } + 25 x ^ { 2 } - 19 } { 120 x ^ { 2 } }$$

Solve for x

$$x=\frac{\sqrt{551}}{29}\approx 0.809427213$$

$$x=-\frac{\sqrt{551}}{29}\approx -0.809427213$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 120x^{2}, the least common multiple of 2,120x^{2}.

$$60x^{2}=64x^{2}+25x^{2}-19$$

Combine 64x^{2} and 25x^{2} to get 89x^{2}.

$$60x^{2}=89x^{2}-19$$

Subtract 89x^{2} from both sides.

$$60x^{2}-89x^{2}=-19$$

Combine 60x^{2} and -89x^{2} to get -29x^{2}.

$$-29x^{2}=-19$$

Divide both sides by -29.

$$x^{2}=\frac{-19}{-29}$$

Fraction \frac{-19}{-29} can be simplified to \frac{19}{29} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{19}{29}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{551}}{29} x=-\frac{\sqrt{551}}{29}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 120x^{2}, the least common multiple of 2,120x^{2}.

$$60x^{2}=64x^{2}+25x^{2}-19$$

Combine 64x^{2} and 25x^{2} to get 89x^{2}.

$$60x^{2}=89x^{2}-19$$

Subtract 89x^{2} from both sides.

$$60x^{2}-89x^{2}=-19$$

Combine 60x^{2} and -89x^{2} to get -29x^{2}.

$$-29x^{2}=-19$$

Add 19 to both sides.

$$-29x^{2}+19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -29 for a, 0 for b, and 19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-29\right)\times 19}}{2\left(-29\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-29\right)\times 19}}{2\left(-29\right)}$$

Multiply -4 times -29.

$$x=\frac{0±\sqrt{116\times 19}}{2\left(-29\right)}$$

Multiply 116 times 19.

$$x=\frac{0±\sqrt{2204}}{2\left(-29\right)}$$

Take the square root of 2204.

$$x=\frac{0±2\sqrt{551}}{2\left(-29\right)}$$

Multiply 2 times -29.

$$x=\frac{0±2\sqrt{551}}{-58}$$

Now solve the equation x=\frac{0±2\sqrt{551}}{-58} when ± is plus.

$$x=-\frac{\sqrt{551}}{29}$$

Now solve the equation x=\frac{0±2\sqrt{551}}{-58} when ± is minus.

$$x=\frac{\sqrt{551}}{29}$$

The equation is now solved.

$$x=-\frac{\sqrt{551}}{29} x=\frac{\sqrt{551}}{29}$$