Solve 49a^2-25=0

$$49 a ^ { 2 } - 25 = 0$$

Solve for a

$$a=\frac{5}{7}\approx 0.714285714$$

$$a=-\frac{5}{7}\approx -0.714285714$$

Steps Using Difference of Squares

Consider 49a^{2}-25. Rewrite 49a^{2}-25 as \left(7a\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).

$$\left(7a-5\right)\left(7a+5\right)=0$$

To find equation solutions, solve 7a-5=0 and 7a+5=0.

$$a=\frac{5}{7} a=-\frac{5}{7}$$

Steps by Finding Square Root

Add 25 to both sides. Anything plus zero gives itself.

$$49a^{2}=25$$

Divide both sides by 49.

$$a^{2}=\frac{25}{49}$$

Take the square root of both sides of the equation.

$$a=\frac{5}{7} a=-\frac{5}{7}$$

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.

$$49a^{2}-25=0$$

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

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

Square 0.

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

Multiply -4 times 49.

$$a=\frac{0±\sqrt{-196\left(-25\right)}}{2\times 49}$$

Multiply -196 times -25.

$$a=\frac{0±\sqrt{4900}}{2\times 49}$$

Take the square root of 4900.

$$a=\frac{0±70}{2\times 49}$$

Multiply 2 times 49.

$$a=\frac{0±70}{98}$$

Now solve the equation a=\frac{0±70}{98} when ± is plus. Reduce the fraction \frac{70}{98} to lowest terms by extracting and canceling out 14.

$$a=\frac{5}{7}$$

Now solve the equation a=\frac{0±70}{98} when ± is minus. Reduce the fraction \frac{-70}{98} to lowest terms by extracting and canceling out 14.

$$a=-\frac{5}{7}$$

The equation is now solved.

$$a=\frac{5}{7} a=-\frac{5}{7}$$