Solve 49c^2-9=0

$$49 c ^ { 2 } - 9 = 0$$

Solve for c

$$c=\frac{3}{7}\approx 0.428571429$$

$$c=-\frac{3}{7}\approx -0.428571429$$

Steps Using Difference of Squares

Consider 49c^{2}-9. Rewrite 49c^{2}-9 as \left(7c\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7c-3\right)\left(7c+3\right)=0$$

To find equation solutions, solve 7c-3=0 and 7c+3=0.

$$c=\frac{3}{7} c=-\frac{3}{7}$$

Steps by Finding Square Root

Add 9 to both sides. Anything plus zero gives itself.

$$49c^{2}=9$$

Divide both sides by 49.

$$c^{2}=\frac{9}{49}$$

Take the square root of both sides of the equation.

$$c=\frac{3}{7} c=-\frac{3}{7}$$

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.

$$49c^{2}-9=0$$

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

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

Square 0.

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

Multiply -4 times 49.

$$c=\frac{0±\sqrt{-196\left(-9\right)}}{2\times 49}$$

Multiply -196 times -9.

$$c=\frac{0±\sqrt{1764}}{2\times 49}$$

Take the square root of 1764.

$$c=\frac{0±42}{2\times 49}$$

Multiply 2 times 49.

$$c=\frac{0±42}{98}$$

Now solve the equation c=\frac{0±42}{98} when ± is plus. Reduce the fraction \frac{42}{98} to lowest terms by extracting and canceling out 14.

$$c=\frac{3}{7}$$

Now solve the equation c=\frac{0±42}{98} when ± is minus. Reduce the fraction \frac{-42}{98} to lowest terms by extracting and canceling out 14.

$$c=-\frac{3}{7}$$

The equation is now solved.

$$c=\frac{3}{7} c=-\frac{3}{7}$$