Solve 9x^2-1=24

$$9 x ^ { 2 } - 1 = 24$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

Steps Using Difference of Squares

Subtract 24 from both sides.

$$9x^{2}-1-24=0$$

Subtract 24 from -1 to get -25.

$$9x^{2}-25=0$$

Consider 9x^{2}-25. Rewrite 9x^{2}-25 as \left(3x\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-5\right)\left(3x+5\right)=0$$

To find equation solutions, solve 3x-5=0 and 3x+5=0.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Steps by Finding Square Root

Add 1 to both sides.

$$9x^{2}=24+1$$

Add 24 and 1 to get 25.

$$9x^{2}=25$$

Divide both sides by 9.

$$x^{2}=\frac{25}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Steps Using the Quadratic Formula

Subtract 24 from both sides.

$$9x^{2}-1-24=0$$

Subtract 24 from -1 to get -25.

$$9x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-25\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-25\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-25\right)}}{2\times 9}$$

Multiply -36 times -25.

$$x=\frac{0±\sqrt{900}}{2\times 9}$$

Take the square root of 900.

$$x=\frac{0±30}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±30}{18}$$

Now solve the equation x=\frac{0±30}{18} when ± is plus. Reduce the fraction \frac{30}{18} to lowest terms by extracting and canceling out 6.

$$x=\frac{5}{3}$$

Now solve the equation x=\frac{0±30}{18} when ± is minus. Reduce the fraction \frac{-30}{18} to lowest terms by extracting and canceling out 6.

$$x=-\frac{5}{3}$$

The equation is now solved.

$$x=\frac{5}{3} x=-\frac{5}{3}$$