Solve 100a^2+4=85

$$100 a ^ { 2 } + 4 = 85$$

Solve for a

$$a=\frac{9}{10}=0.9$$

$$a=-\frac{9}{10}=-0.9$$

Steps Using Difference of Squares

Subtract 85 from both sides.

$$100a^{2}+4-85=0$$

Subtract 85 from 4 to get -81.

$$100a^{2}-81=0$$

Consider 100a^{2}-81. Rewrite 100a^{2}-81 as \left(10a\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(10a-9\right)\left(10a+9\right)=0$$

To find equation solutions, solve 10a-9=0 and 10a+9=0.

$$a=\frac{9}{10} a=-\frac{9}{10}$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$100a^{2}=85-4$$

Subtract 4 from 85 to get 81.

$$100a^{2}=81$$

Divide both sides by 100.

$$a^{2}=\frac{81}{100}$$

Take the square root of both sides of the equation.

$$a=\frac{9}{10} a=-\frac{9}{10}$$

Steps Using the Quadratic Formula

Subtract 85 from both sides.

$$100a^{2}+4-85=0$$

Subtract 85 from 4 to get -81.

$$100a^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 100\left(-81\right)}}{2\times 100}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 100\left(-81\right)}}{2\times 100}$$

Multiply -4 times 100.

$$a=\frac{0±\sqrt{-400\left(-81\right)}}{2\times 100}$$

Multiply -400 times -81.

$$a=\frac{0±\sqrt{32400}}{2\times 100}$$

Take the square root of 32400.

$$a=\frac{0±180}{2\times 100}$$

Multiply 2 times 100.

$$a=\frac{0±180}{200}$$

Now solve the equation a=\frac{0±180}{200} when ± is plus. Reduce the fraction \frac{180}{200} to lowest terms by extracting and canceling out 20.

$$a=\frac{9}{10}$$

Now solve the equation a=\frac{0±180}{200} when ± is minus. Reduce the fraction \frac{-180}{200} to lowest terms by extracting and canceling out 20.

$$a=-\frac{9}{10}$$

The equation is now solved.

$$a=\frac{9}{10} a=-\frac{9}{10}$$