Solve 8x^2/49=74

$$\frac { 8 x ^ { 2 } } { 49 } = 74$$

Solve for x

$$x = \frac{7 \sqrt{37}}{2} \approx 21.289668856$$

$$x = -\frac{7 \sqrt{37}}{2} \approx -21.289668856$$

Steps by Finding Square Root

Multiply both sides by 49.

$$8x^{2}=74\times 49$$

Multiply 74 and 49 to get 3626.

$$8x^{2}=3626$$

Divide both sides by 8.

$$x^{2}=\frac{3626}{8}$$

Reduce the fraction \frac{3626}{8} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{1813}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{7\sqrt{37}}{2} x=-\frac{7\sqrt{37}}{2}$$

Steps Using the Quadratic Formula

Multiply both sides by 49.

$$8x^{2}=74\times 49$$

Multiply 74 and 49 to get 3626.

$$8x^{2}=3626$$

Subtract 3626 from both sides.

$$8x^{2}-3626=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -3626 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-3626\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-3626\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-3626\right)}}{2\times 8}$$

Multiply -32 times -3626.

$$x=\frac{0±\sqrt{116032}}{2\times 8}$$

Take the square root of 116032.

$$x=\frac{0±56\sqrt{37}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±56\sqrt{37}}{16}$$

Now solve the equation x=\frac{0±56\sqrt{37}}{16} when ± is plus.

$$x=\frac{7\sqrt{37}}{2}$$

Now solve the equation x=\frac{0±56\sqrt{37}}{16} when ± is minus.

$$x=-\frac{7\sqrt{37}}{2}$$

The equation is now solved.

$$x=\frac{7\sqrt{37}}{2} x=-\frac{7\sqrt{37}}{2}$$