Solve 7x^2-9x^2=+17-48

$$7 { x }^{ 2 } -9 { x }^{ 2 } =+17-48$$

Solve for x

$$x = \frac{\sqrt{62}}{2} \approx 3.937003937$$

$$x = -\frac{\sqrt{62}}{2} \approx -3.937003937$$

Steps by Finding Square Root

Combine 7x^{2} and -9x^{2} to get -2x^{2}.

$$-2x^{2}=17-48$$

Subtract 48 from 17 to get -31.

$$-2x^{2}=-31$$

Divide both sides by -2.

$$x^{2}=\frac{-31}{-2}$$

Fraction \frac{-31}{-2} can be simplified to \frac{31}{2} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{31}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{62}}{2} x=-\frac{\sqrt{62}}{2}$$

Steps Using the Quadratic Formula

Combine 7x^{2} and -9x^{2} to get -2x^{2}.

$$-2x^{2}=17-48$$

Subtract 48 from 17 to get -31.

$$-2x^{2}=-31$$

Add 31 to both sides.

$$-2x^{2}+31=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 31 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 31}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 31}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 31}}{2\left(-2\right)}$$

Multiply 8 times 31.

$$x=\frac{0±\sqrt{248}}{2\left(-2\right)}$$

Take the square root of 248.

$$x=\frac{0±2\sqrt{62}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±2\sqrt{62}}{-4}$$

Now solve the equation x=\frac{0±2\sqrt{62}}{-4} when ± is plus.

$$x=-\frac{\sqrt{62}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{62}}{-4} when ± is minus.

$$x=\frac{\sqrt{62}}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{62}}{2} x=\frac{\sqrt{62}}{2}$$