Solve 16*4-136x^2+225=0

$$16 \times 4 - 136 x ^ { 2 } + 225 = 0$$

Solve for x

$$x = \frac{\sqrt{34}}{4} \approx 1.457737974$$

$$x = -\frac{\sqrt{34}}{4} \approx -1.457737974$$

Steps by Finding Square Root

Multiply 16 and 4 to get 64.

$$64-136x^{2}+225=0$$

Add 64 and 225 to get 289.

$$289-136x^{2}=0$$

Subtract 289 from both sides. Anything subtracted from zero gives its negation.

$$-136x^{2}=-289$$

Divide both sides by -136.

$$x^{2}=\frac{-289}{-136}$$

Reduce the fraction \frac{-289}{-136} to lowest terms by extracting and canceling out -17.

$$x^{2}=\frac{17}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{34}}{4} x=-\frac{\sqrt{34}}{4}$$

Steps Using the Quadratic Formula

Multiply 16 and 4 to get 64.

$$64-136x^{2}+225=0$$

Add 64 and 225 to get 289.

$$289-136x^{2}=0$$

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.

$$-136x^{2}+289=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -136 for a, 0 for b, and 289 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-136\right)\times 289}}{2\left(-136\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-136\right)\times 289}}{2\left(-136\right)}$$

Multiply -4 times -136.

$$x=\frac{0±\sqrt{544\times 289}}{2\left(-136\right)}$$

Multiply 544 times 289.

$$x=\frac{0±\sqrt{157216}}{2\left(-136\right)}$$

Take the square root of 157216.

$$x=\frac{0±68\sqrt{34}}{2\left(-136\right)}$$

Multiply 2 times -136.

$$x=\frac{0±68\sqrt{34}}{-272}$$

Now solve the equation x=\frac{0±68\sqrt{34}}{-272} when ± is plus.

$$x=-\frac{\sqrt{34}}{4}$$

Now solve the equation x=\frac{0±68\sqrt{34}}{-272} when ± is minus.

$$x=\frac{\sqrt{34}}{4}$$

The equation is now solved.

$$x=-\frac{\sqrt{34}}{4} x=\frac{\sqrt{34}}{4}$$