Solve a^2=1.2^2+0.9^2

$$a ^ { 2 } = 1.2 ^ { 2 } + 0.9 ^ { 2 }$$

Solve for a

$$a=-1.5$$

$$a=1.5$$

Steps Using Difference of Squares

Calculate 1.2 to the power of 2 and get 1.44.

$$a^{2}=1.44+0.9^{2}$$

Calculate 0.9 to the power of 2 and get 0.81.

$$a^{2}=1.44+0.81$$

Add 1.44 and 0.81 to get 2.25.

$$a^{2}=2.25$$

Subtract 2.25 from both sides.

$$a^{2}-2.25=0$$

Consider a^{2}-2.25. Rewrite a^{2}-2.25 as a^{2}-\left(\frac{3}{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-\frac{3}{2}\right)\left(a+\frac{3}{2}\right)=0$$

To find equation solutions, solve a-\frac{3}{2}=0 and a+\frac{3}{2}=0.

$$a=\frac{3}{2} a=-\frac{3}{2}$$

Steps by Finding Square Root

Calculate 1.2 to the power of 2 and get 1.44.

$$a^{2}=1.44+0.9^{2}$$

Calculate 0.9 to the power of 2 and get 0.81.

$$a^{2}=1.44+0.81$$

Add 1.44 and 0.81 to get 2.25.

$$a^{2}=2.25$$

Take the square root of both sides of the equation.

$$a=\frac{3}{2} a=-\frac{3}{2}$$

Steps Using the Quadratic Formula

Calculate 1.2 to the power of 2 and get 1.44.

$$a^{2}=1.44+0.9^{2}$$

Calculate 0.9 to the power of 2 and get 0.81.

$$a^{2}=1.44+0.81$$

Add 1.44 and 0.81 to get 2.25.

$$a^{2}=2.25$$

Subtract 2.25 from both sides.

$$a^{2}-2.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-2.25\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-2.25\right)}}{2}$$

Multiply -4 times -2.25.

$$a=\frac{0±\sqrt{9}}{2}$$

Take the square root of 9.

$$a=\frac{0±3}{2}$$

Now solve the equation a=\frac{0±3}{2} when ± is plus. Divide 3 by 2.

$$a=\frac{3}{2}$$

Now solve the equation a=\frac{0±3}{2} when ± is minus. Divide -3 by 2.

$$a=-\frac{3}{2}$$

The equation is now solved.

$$a=\frac{3}{2} a=-\frac{3}{2}$$