Solve 9.8*4=x^2-(4.2)^2

$$9.8 \times 4 = x ^ { 2 } - ( 4.2 ) ^ { 2 }$$

Solve for x

$$x = \frac{7 \sqrt{29}}{5} \approx 7.53923073$$

$$x = -\frac{7 \sqrt{29}}{5} \approx -7.53923073$$

Steps by Finding Square Root

Multiply 9.8 and 4 to get 39.2.

$$39.2=x^{2}-4.2^{2}$$

Calculate 4.2 to the power of 2 and get 17.64.

$$39.2=x^{2}-17.64$$

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

$$x^{2}-17.64=39.2$$

Add 17.64 to both sides.

$$x^{2}=39.2+17.64$$

Add 39.2 and 17.64 to get 56.84.

$$x^{2}=56.84$$

Take the square root of both sides of the equation.

$$x=\frac{7\sqrt{29}}{5} x=-\frac{7\sqrt{29}}{5}$$

Steps Using the Quadratic Formula

Multiply 9.8 and 4 to get 39.2.

$$39.2=x^{2}-4.2^{2}$$

Calculate 4.2 to the power of 2 and get 17.64.

$$39.2=x^{2}-17.64$$

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

$$x^{2}-17.64=39.2$$

Subtract 39.2 from both sides.

$$x^{2}-17.64-39.2=0$$

Subtract 39.2 from -17.64 to get -56.84.

$$x^{2}-56.84=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -56.84 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-56.84\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-56.84\right)}}{2}$$

Multiply -4 times -56.84.

$$x=\frac{0±\sqrt{227.36}}{2}$$

Take the square root of 227.36.

$$x=\frac{0±\frac{14\sqrt{29}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{14\sqrt{29}}{5}}{2} when ± is plus.

$$x=\frac{7\sqrt{29}}{5}$$

Now solve the equation x=\frac{0±\frac{14\sqrt{29}}{5}}{2} when ± is minus.

$$x=-\frac{7\sqrt{29}}{5}$$

The equation is now solved.

$$x=\frac{7\sqrt{29}}{5} x=-\frac{7\sqrt{29}}{5}$$