Solve 1/2*2.64*x^2=1/2*97.8*(0.85)^2

$$\frac { 1 } { 2 } \times 2.64 \times x ^ { 2 } = \frac { 1 } { 2 } \times 97.8 \times ( 0.85 ) ^ { 2 }$$

Solve for x

$$x = \frac{17 \sqrt{17930}}{440} \approx 5.173523065$$

$$x = -\frac{17 \sqrt{17930}}{440} \approx -5.173523065$$

Steps by Finding Square Root

Cancel out \frac{1}{2} on both sides.

$$2.64x^{2}=97.8\times 0.85^{2}$$

Calculate 0.85 to the power of 2 and get 0.7225.

$$2.64x^{2}=97.8\times 0.7225$$

Multiply 97.8 and 0.7225 to get 70.6605.

$$2.64x^{2}=70.6605$$

Divide both sides by 2.64.

$$x^{2}=\frac{70.6605}{2.64}$$

Expand \frac{70.6605}{2.64} by multiplying both numerator and the denominator by 10000.

$$x^{2}=\frac{706605}{26400}$$

Reduce the fraction \frac{706605}{26400} to lowest terms by extracting and canceling out 15.

$$x^{2}=\frac{47107}{1760}$$

Take the square root of both sides of the equation.

$$x=\frac{17\sqrt{17930}}{440} x=-\frac{17\sqrt{17930}}{440}$$

Steps Using the Quadratic Formula

Cancel out \frac{1}{2} on both sides.

$$2.64x^{2}=97.8\times 0.85^{2}$$

Calculate 0.85 to the power of 2 and get 0.7225.

$$2.64x^{2}=97.8\times 0.7225$$

Multiply 97.8 and 0.7225 to get 70.6605.

$$2.64x^{2}=70.6605$$

Subtract 70.6605 from both sides.

$$2.64x^{2}-70.6605=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2.64 for a, 0 for b, and -70.6605 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2.64\left(-70.6605\right)}}{2\times 2.64}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2.64\left(-70.6605\right)}}{2\times 2.64}$$

Multiply -4 times 2.64.

$$x=\frac{0±\sqrt{-10.56\left(-70.6605\right)}}{2\times 2.64}$$

Multiply -10.56 times -70.6605 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{746.17488}}{2\times 2.64}$$

Take the square root of 746.17488.

$$x=\frac{0±\frac{51\sqrt{17930}}{250}}{2\times 2.64}$$

Multiply 2 times 2.64.

$$x=\frac{0±\frac{51\sqrt{17930}}{250}}{5.28}$$

Now solve the equation x=\frac{0±\frac{51\sqrt{17930}}{250}}{5.28} when ± is plus.

$$x=\frac{17\sqrt{17930}}{440}$$

Now solve the equation x=\frac{0±\frac{51\sqrt{17930}}{250}}{5.28} when ± is minus.

$$x=-\frac{17\sqrt{17930}}{440}$$

The equation is now solved.

$$x=\frac{17\sqrt{17930}}{440} x=-\frac{17\sqrt{17930}}{440}$$