Solve 16-x^2=1

$$16 - x ^ { 2 } = 1$$

Solve for x

$$x=\sqrt{15}\approx 3.872983346$$

$$x=-\sqrt{15}\approx -3.872983346$$

Steps by Finding Square Root

Subtract 16 from both sides.

$$-x^{2}=1-16$$

Subtract 16 from 1 to get -15.

$$-x^{2}=-15$$

Divide both sides by -1.

$$x^{2}=\frac{-15}{-1}$$

Fraction \frac{-15}{-1} can be simplified to 15 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=15$$

Take the square root of both sides of the equation.

$$x=\sqrt{15} x=-\sqrt{15}$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$16-x^{2}-1=0$$

Subtract 1 from 16 to get 15.

$$15-x^{2}=0$$

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.

$$-x^{2}+15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 15}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 15}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 15}}{2\left(-1\right)}$$

Multiply 4 times 15.

$$x=\frac{0±\sqrt{60}}{2\left(-1\right)}$$

Take the square root of 60.

$$x=\frac{0±2\sqrt{15}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{15}}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{-2} when ± is plus.

$$x=-\sqrt{15}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{-2} when ± is minus.

$$x=\sqrt{15}$$

The equation is now solved.

$$x=-\sqrt{15} x=\sqrt{15}$$