Solve 9x^2-37x^2+4=0

$$9 x ^ { 2 } - 37 x ^ { 2 } + 4 = 0$$

Solve for x

$$x=\frac{\sqrt{7}}{7}\approx 0.377964473$$

$$x=-\frac{\sqrt{7}}{7}\approx -0.377964473$$

Steps by Finding Square Root

Combine 9x^{2} and -37x^{2} to get -28x^{2}.

$$-28x^{2}+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-28x^{2}=-4$$

Divide both sides by -28.

$$x^{2}=\frac{-4}{-28}$$

Reduce the fraction \frac{-4}{-28} to lowest terms by extracting and canceling out -4.

$$x^{2}=\frac{1}{7}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Combine 9x^{2} and -37x^{2} to get -28x^{2}.

$$-28x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -28 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-28\right)\times 4}}{2\left(-28\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-28\right)\times 4}}{2\left(-28\right)}$$

Multiply -4 times -28.

$$x=\frac{0±\sqrt{112\times 4}}{2\left(-28\right)}$$

Multiply 112 times 4.

$$x=\frac{0±\sqrt{448}}{2\left(-28\right)}$$

Take the square root of 448.

$$x=\frac{0±8\sqrt{7}}{2\left(-28\right)}$$

Multiply 2 times -28.

$$x=\frac{0±8\sqrt{7}}{-56}$$

Now solve the equation x=\frac{0±8\sqrt{7}}{-56} when ± is plus.

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

Now solve the equation x=\frac{0±8\sqrt{7}}{-56} when ± is minus.

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

The equation is now solved.

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