Solve 16x^2=49

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

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

$$x = -\frac{7}{4} = -1\frac{3}{4} = -1.75$$

Steps Using Difference of Squares

Divide both sides by 16.

$$x^{2}=\frac{49}{16}$$

Subtract \frac{49}{16} from both sides.

$$x^{2}-\frac{49}{16}=0$$

Multiply both sides by 16.

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

Consider 16x^{2}-49. Rewrite 16x^{2}-49 as \left(4x\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4x-7\right)\left(4x+7\right)=0$$

To find equation solutions, solve 4x-7=0 and 4x+7=0.

$$x=\frac{7}{4} x=-\frac{7}{4}$$

Steps by Finding Square Root

Divide both sides by 16.

$$x^{2}=\frac{49}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{4} x=-\frac{7}{4}$$

Steps Using the Quadratic Formula

Divide both sides by 16.

$$x^{2}=\frac{49}{16}$$

Subtract \frac{49}{16} from both sides.

$$x^{2}-\frac{49}{16}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{49}{16} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{16}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{49}{16}\right)}}{2}$$

Multiply -4 times -\frac{49}{16}.

$$x=\frac{0±\sqrt{\frac{49}{4}}}{2}$$

Take the square root of \frac{49}{4}.

$$x=\frac{0±\frac{7}{2}}{2}$$

Now solve the equation x=\frac{0±\frac{7}{2}}{2} when ± is plus.

$$x=\frac{7}{4}$$

Now solve the equation x=\frac{0±\frac{7}{2}}{2} when ± is minus.

$$x=-\frac{7}{4}$$

The equation is now solved.

$$x=\frac{7}{4} x=-\frac{7}{4}$$