Solve 30=x*1.45x

$$30=x \times 1.45x$$

Solve for x

$$x = \frac{10 \sqrt{174}}{29} \approx 4.548588261$$

$$x = -\frac{10 \sqrt{174}}{29} \approx -4.548588261$$

Steps by Finding Square Root

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

$$30=x^{2}\times 1.45$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\times 1.45=30$$

Divide both sides by 1.45.

$$x^{2}=\frac{30}{1.45}$$

Expand \frac{30}{1.45} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{3000}{145}$$

Reduce the fraction \frac{3000}{145} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{600}{29}$$

Take the square root of both sides of the equation.

$$x=\frac{10\sqrt{174}}{29} x=-\frac{10\sqrt{174}}{29}$$

Steps Using the Quadratic Formula

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

$$30=x^{2}\times 1.45$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\times 1.45=30$$

Subtract 30 from both sides.

$$x^{2}\times 1.45-30=0$$

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.

$$1.45x^{2}-30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.45 for a, 0 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1.45\left(-30\right)}}{2\times 1.45}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1.45\left(-30\right)}}{2\times 1.45}$$

Multiply -4 times 1.45.

$$x=\frac{0±\sqrt{-5.8\left(-30\right)}}{2\times 1.45}$$

Multiply -5.8 times -30.

$$x=\frac{0±\sqrt{174}}{2\times 1.45}$$

Multiply 2 times 1.45.

$$x=\frac{0±\sqrt{174}}{2.9}$$

Now solve the equation x=\frac{0±\sqrt{174}}{2.9} when ± is plus.

$$x=\frac{10\sqrt{174}}{29}$$

Now solve the equation x=\frac{0±\sqrt{174}}{2.9} when ± is minus.

$$x=-\frac{10\sqrt{174}}{29}$$

The equation is now solved.

$$x=\frac{10\sqrt{174}}{29} x=-\frac{10\sqrt{174}}{29}$$