Solve x^2+x^2=1.5^2

$${ x }^{ 2 } + { x }^{ 2 } = { 1.5 }^{ 2 }$$

Solve for x

$$x = \frac{3 \sqrt{2}}{4} \approx 1.060660172$$

$$x = -\frac{3 \sqrt{2}}{4} \approx -1.060660172$$

Steps by Finding Square Root

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}=1.5^{2}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$2x^{2}=2.25$$

Divide both sides by 2.

$$x^{2}=\frac{2.25}{2}$$

Expand \frac{2.25}{2} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{225}{200}$$

Reduce the fraction \frac{225}{200} to lowest terms by extracting and canceling out 25.

$$x^{2}=\frac{9}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{2}}{4} x=-\frac{3\sqrt{2}}{4}$$

Steps Using the Quadratic Formula

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}=1.5^{2}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$2x^{2}=2.25$$

Subtract 2.25 from both sides.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-2.25\right)}}{2\times 2}$$

Multiply -8 times -2.25.

$$x=\frac{0±\sqrt{18}}{2\times 2}$$

Take the square root of 18.

$$x=\frac{0±3\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±3\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±3\sqrt{2}}{4} when ± is plus.

$$x=\frac{3\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±3\sqrt{2}}{4} when ± is minus.

$$x=-\frac{3\sqrt{2}}{4}$$

The equation is now solved.

$$x=\frac{3\sqrt{2}}{4} x=-\frac{3\sqrt{2}}{4}$$