Solve x^2+0.36x^2=225

$$x ^ { 2 } + 0.36 x ^ { 2 } = 225$$

Solve for x

$$x = \frac{75 \sqrt{34}}{34} \approx 12.862393886$$

$$x = -\frac{75 \sqrt{34}}{34} \approx -12.862393886$$

Steps by Finding Square Root

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

$$1.36x^{2}=225$$

Divide both sides by 1.36.

$$x^{2}=\frac{225}{1.36}$$

Expand \frac{225}{1.36} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{22500}{136}$$

Reduce the fraction \frac{22500}{136} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{5625}{34}$$

Take the square root of both sides of the equation.

$$x=\frac{75\sqrt{34}}{34} x=-\frac{75\sqrt{34}}{34}$$

Steps Using the Quadratic Formula

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

$$1.36x^{2}=225$$

Subtract 225 from both sides.

$$1.36x^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.36 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1.36\left(-225\right)}}{2\times 1.36}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1.36\left(-225\right)}}{2\times 1.36}$$

Multiply -4 times 1.36.

$$x=\frac{0±\sqrt{-5.44\left(-225\right)}}{2\times 1.36}$$

Multiply -5.44 times -225.

$$x=\frac{0±\sqrt{1224}}{2\times 1.36}$$

Take the square root of 1224.

$$x=\frac{0±6\sqrt{34}}{2\times 1.36}$$

Multiply 2 times 1.36.

$$x=\frac{0±6\sqrt{34}}{2.72}$$

Now solve the equation x=\frac{0±6\sqrt{34}}{2.72} when ± is plus.

$$x=\frac{75\sqrt{34}}{34}$$

Now solve the equation x=\frac{0±6\sqrt{34}}{2.72} when ± is minus.

$$x=-\frac{75\sqrt{34}}{34}$$

The equation is now solved.

$$x=\frac{75\sqrt{34}}{34} x=-\frac{75\sqrt{34}}{34}$$