Solve x^2+(0.6x)^2=15

$$x ^ { 2 } + ( 0.6 x ) ^ { 2 } = 15$$

Solve for x

$$x = \frac{5 \sqrt{510}}{34} \approx 3.321055821$$

$$x = -\frac{5 \sqrt{510}}{34} \approx -3.321055821$$

Steps by Finding Square Root

Expand \left(0.6x\right)^{2}.

$$x^{2}+0.6^{2}x^{2}=15$$

Calculate 0.6 to the power of 2 and get 0.36.

$$x^{2}+0.36x^{2}=15$$

Combine x^{2} and 0.36x^{2} to get 1.36x^{2}.

$$1.36x^{2}=15$$

Divide both sides by 1.36.

$$x^{2}=\frac{15}{1.36}$$

Expand \frac{15}{1.36} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{1500}{136}$$

Reduce the fraction \frac{1500}{136} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{375}{34}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{510}}{34} x=-\frac{5\sqrt{510}}{34}$$

Steps Using the Quadratic Formula

Expand \left(0.6x\right)^{2}.

$$x^{2}+0.6^{2}x^{2}=15$$

Calculate 0.6 to the power of 2 and get 0.36.

$$x^{2}+0.36x^{2}=15$$

Combine x^{2} and 0.36x^{2} to get 1.36x^{2}.

$$1.36x^{2}=15$$

Subtract 15 from both sides.

$$1.36x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.36 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1.36\left(-15\right)}}{2\times 1.36}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1.36\left(-15\right)}}{2\times 1.36}$$

Multiply -4 times 1.36.

$$x=\frac{0±\sqrt{-5.44\left(-15\right)}}{2\times 1.36}$$

Multiply -5.44 times -15.

$$x=\frac{0±\sqrt{81.6}}{2\times 1.36}$$

Take the square root of 81.6.

$$x=\frac{0±\frac{2\sqrt{510}}{5}}{2\times 1.36}$$

Multiply 2 times 1.36.

$$x=\frac{0±\frac{2\sqrt{510}}{5}}{2.72}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{510}}{5}}{2.72} when ± is plus.

$$x=\frac{5\sqrt{510}}{34}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{510}}{5}}{2.72} when ± is minus.

$$x=-\frac{5\sqrt{510}}{34}$$

The equation is now solved.

$$x=\frac{5\sqrt{510}}{34} x=-\frac{5\sqrt{510}}{34}$$