Solve 16x^2+49=100

$$16 x ^ { 2 } + 49 = 100$$

Solve for x

$$x = \frac{\sqrt{51}}{4} \approx 1.785357107$$

$$x = -\frac{\sqrt{51}}{4} \approx -1.785357107$$

Steps by Finding Square Root

Subtract 49 from both sides.

$$16x^{2}=100-49$$

Subtract 49 from 100 to get 51.

$$16x^{2}=51$$

Divide both sides by 16.

$$x^{2}=\frac{51}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{51}}{4} x=-\frac{\sqrt{51}}{4}$$

Steps Using the Quadratic Formula

Subtract 100 from both sides.

$$16x^{2}+49-100=0$$

Subtract 100 from 49 to get -51.

$$16x^{2}-51=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -51 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-51\right)}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-51\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\left(-51\right)}}{2\times 16}$$

Multiply -64 times -51.

$$x=\frac{0±\sqrt{3264}}{2\times 16}$$

Take the square root of 3264.

$$x=\frac{0±8\sqrt{51}}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±8\sqrt{51}}{32}$$

Now solve the equation x=\frac{0±8\sqrt{51}}{32} when ± is plus.

$$x=\frac{\sqrt{51}}{4}$$

Now solve the equation x=\frac{0±8\sqrt{51}}{32} when ± is minus.

$$x=-\frac{\sqrt{51}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{51}}{4} x=-\frac{\sqrt{51}}{4}$$