Solve 100x^2-49=0

$$100 x ^ { 2 } - 49 = 0$$

Solve for x

$$x=\frac{7}{10}=0.7$$

$$x=-\frac{7}{10}=-0.7$$

Steps Using Difference of Squares

Consider 100x^{2}-49. Rewrite 100x^{2}-49 as \left(10x\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(10x-7\right)\left(10x+7\right)=0$$

To find equation solutions, solve 10x-7=0 and 10x+7=0.

$$x=\frac{7}{10} x=-\frac{7}{10}$$

Steps by Finding Square Root

Add 49 to both sides. Anything plus zero gives itself.

$$100x^{2}=49$$

Divide both sides by 100.

$$x^{2}=\frac{49}{100}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{10} x=-\frac{7}{10}$$

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.

$$100x^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 100\left(-49\right)}}{2\times 100}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 100\left(-49\right)}}{2\times 100}$$

Multiply -4 times 100.

$$x=\frac{0±\sqrt{-400\left(-49\right)}}{2\times 100}$$

Multiply -400 times -49.

$$x=\frac{0±\sqrt{19600}}{2\times 100}$$

Take the square root of 19600.

$$x=\frac{0±140}{2\times 100}$$

Multiply 2 times 100.

$$x=\frac{0±140}{200}$$

Now solve the equation x=\frac{0±140}{200} when ± is plus. Reduce the fraction \frac{140}{200} to lowest terms by extracting and canceling out 20.

$$x=\frac{7}{10}$$

Now solve the equation x=\frac{0±140}{200} when ± is minus. Reduce the fraction \frac{-140}{200} to lowest terms by extracting and canceling out 20.

$$x=-\frac{7}{10}$$

The equation is now solved.

$$x=\frac{7}{10} x=-\frac{7}{10}$$