Solve (1.4)^2+x^2=5^2

$$( 1.4 ) ^ { 2 } + x ^ { 2 } = 5 ^ { 2 }$$

Solve for x

$$x=4.8$$

$$x=-4.8$$

Steps Using Difference of Squares

Calculate 1.4 to the power of 2 and get 1.96.

$$1.96+x^{2}=5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$1.96+x^{2}=25$$

Subtract 25 from both sides.

$$1.96+x^{2}-25=0$$

Subtract 25 from 1.96 to get -23.04.

$$-23.04+x^{2}=0$$

Consider -23.04+x^{2}. Rewrite -23.04+x^{2} as x^{2}-\left(\frac{24}{5}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{24}{5}\right)\left(x+\frac{24}{5}\right)=0$$

To find equation solutions, solve x-\frac{24}{5}=0 and x+\frac{24}{5}=0.

$$x=\frac{24}{5} x=-\frac{24}{5}$$

Steps by Finding Square Root

Calculate 1.4 to the power of 2 and get 1.96.

$$1.96+x^{2}=5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$1.96+x^{2}=25$$

Subtract 1.96 from both sides.

$$x^{2}=25-1.96$$

Subtract 1.96 from 25 to get 23.04.

$$x^{2}=23.04$$

Take the square root of both sides of the equation.

$$x=\frac{24}{5} x=-\frac{24}{5}$$

Steps Using the Quadratic Formula

Calculate 1.4 to the power of 2 and get 1.96.

$$1.96+x^{2}=5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$1.96+x^{2}=25$$

Subtract 25 from both sides.

$$1.96+x^{2}-25=0$$

Subtract 25 from 1.96 to get -23.04.

$$-23.04+x^{2}=0$$

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.

$$x^{2}-23.04=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -23.04 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-23.04\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-23.04\right)}}{2}$$

Multiply -4 times -23.04.

$$x=\frac{0±\sqrt{92.16}}{2}$$

Take the square root of 92.16.

$$x=\frac{0±\frac{48}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{48}{5}}{2} when ± is plus.

$$x=\frac{24}{5}$$

Now solve the equation x=\frac{0±\frac{48}{5}}{2} when ± is minus.

$$x=-\frac{24}{5}$$

The equation is now solved.

$$x=\frac{24}{5} x=-\frac{24}{5}$$