Solve cos70^circ=x^2+x^2-10^2/2(x)(x)

$$\cos 70 ^ { \circ } = \frac { x ^ { 2 } + x ^ { 2 } - 10 ^ { 2 } } { 2 ( x ) ( x ) }$$

Solve for x

$$x = \frac{125000000 \sqrt{822474820842914}}{411237410421457} = 8\frac{294953443822382}{411237410421457} \approx 8.717233978$$

$$x = -\frac{125000000 \sqrt{822474820842914}}{411237410421457} = -8\frac{294953443822382}{411237410421457} \approx -8.717233978$$

Steps by Finding Square Root

Evaluate trigonometric functions in the problem

$$0.3420201433256688 = \frac{x ^ {2} + x ^ {2} - 10 ^ {2}}{2 {(x)} {(x)}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x^{2}.

$$0.6840402866513376x^{2}=x^{2}+x^{2}-10^{2}$$

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

$$0.6840402866513376x^{2}=2x^{2}-10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$0.6840402866513376x^{2}=2x^{2}-100$$

Subtract 2x^{2} from both sides.

$$0.6840402866513376x^{2}-2x^{2}=-100$$

Combine 0.6840402866513376x^{2} and -2x^{2} to get -1.3159597133486624x^{2}.

$$-1.3159597133486624x^{2}=-100$$

Divide both sides by -1.3159597133486624.

$$x^{2}=\frac{-100}{-1.3159597133486624}$$

Expand \frac{-100}{-1.3159597133486624} by multiplying both numerator and the denominator by 10000000000000000.

$$x^{2}=\frac{-1000000000000000000}{-13159597133486624}$$

Reduce the fraction \frac{-1000000000000000000}{-13159597133486624} to lowest terms by extracting and canceling out -32.

$$x^{2}=\frac{31250000000000000}{411237410421457}$$

Take the square root of both sides of the equation.

$$x=\frac{125000000\sqrt{822474820842914}}{411237410421457} x=-\frac{125000000\sqrt{822474820842914}}{411237410421457}$$

Steps Using the Quadratic Formula

Evaluate trigonometric functions in the problem

$$0.3420201433256688 = \frac{x ^ {2} + x ^ {2} - 10 ^ {2}}{2 {(x)} {(x)}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x^{2}.

$$0.6840402866513376x^{2}=x^{2}+x^{2}-10^{2}$$

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

$$0.6840402866513376x^{2}=2x^{2}-10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$0.6840402866513376x^{2}=2x^{2}-100$$

Subtract 2x^{2} from both sides.

$$0.6840402866513376x^{2}-2x^{2}=-100$$

Combine 0.6840402866513376x^{2} and -2x^{2} to get -1.3159597133486624x^{2}.

$$-1.3159597133486624x^{2}=-100$$

Add 100 to both sides.

$$-1.3159597133486624x^{2}+100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1.3159597133486624 for a, 0 for b, and 100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1.3159597133486624\right)\times 100}}{2\left(-1.3159597133486624\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1.3159597133486624\right)\times 100}}{2\left(-1.3159597133486624\right)}$$

Multiply -4 times -1.3159597133486624.

$$x=\frac{0±\sqrt{5.2638388533946496\times 100}}{2\left(-1.3159597133486624\right)}$$

Multiply 5.2638388533946496 times 100.

$$x=\frac{0±\sqrt{526.38388533946496}}{2\left(-1.3159597133486624\right)}$$

Take the square root of 526.38388533946496.

$$x=\frac{0±\frac{\sqrt{822474820842914}}{1250000}}{2\left(-1.3159597133486624\right)}$$

Multiply 2 times -1.3159597133486624.

$$x=\frac{0±\frac{\sqrt{822474820842914}}{1250000}}{-2.6319194266973248}$$

Now solve the equation x=\frac{0±\frac{\sqrt{822474820842914}}{1250000}}{-2.6319194266973248} when ± is plus.

$$x=-\frac{125000000\sqrt{822474820842914}}{411237410421457}$$

Now solve the equation x=\frac{0±\frac{\sqrt{822474820842914}}{1250000}}{-2.6319194266973248} when ± is minus.

$$x=\frac{125000000\sqrt{822474820842914}}{411237410421457}$$

The equation is now solved.

$$x=-\frac{125000000\sqrt{822474820842914}}{411237410421457} x=\frac{125000000\sqrt{822474820842914}}{411237410421457}$$