Solve 9x^2-25/49=0

$$9 x ^ { 2 } - \frac { 25 } { 49 } = 0$$

Solve for x

$$x=\frac{5}{21}\approx 0.238095238$$

$$x=-\frac{5}{21}\approx -0.238095238$$

Steps Using Difference of Squares

Multiply both sides by 49.

$$441x^{2}-25=0$$

Consider 441x^{2}-25. Rewrite 441x^{2}-25 as \left(21x\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).

$$\left(21x-5\right)\left(21x+5\right)=0$$

To find equation solutions, solve 21x-5=0 and 21x+5=0.

$$x=\frac{5}{21} x=-\frac{5}{21}$$

Steps by Finding Square Root

Add \frac{25}{49} to both sides. Anything plus zero gives itself.

$$9x^{2}=\frac{25}{49}$$

Divide both sides by 9.

$$x^{2}=\frac{\frac{25}{49}}{9}$$

Express \frac{\frac{25}{49}}{9} as a single fraction.

$$x^{2}=\frac{25}{49\times 9}$$

Multiply 49 and 9 to get 441.

$$x^{2}=\frac{25}{441}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{21} x=-\frac{5}{21}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$9x^{2}-\frac{25}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -\frac{25}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-\frac{25}{49}\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-\frac{25}{49}\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-\frac{25}{49}\right)}}{2\times 9}$$

Multiply -36 times -\frac{25}{49}.

$$x=\frac{0±\sqrt{\frac{900}{49}}}{2\times 9}$$

Take the square root of \frac{900}{49}.

$$x=\frac{0±\frac{30}{7}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±\frac{30}{7}}{18}$$

Now solve the equation x=\frac{0±\frac{30}{7}}{18} when ± is plus.

$$x=\frac{5}{21}$$

Now solve the equation x=\frac{0±\frac{30}{7}}{18} when ± is minus.

$$x=-\frac{5}{21}$$

The equation is now solved.

$$x=\frac{5}{21} x=-\frac{5}{21}$$