Solve 20-8x=sqrt{7^2+(-8)^2}*frac{4sqrt{13}}{113}

$$20 - 8 x = \sqrt { 7 ^ { 2 } + ( - 8 ) ^ { 2 } } \cdot \frac { 4 \sqrt { 13 } } { 113 }$$

Solve for x

$$x=-\frac{\sqrt{1469}}{226}+\frac{5}{2}\approx 2.330409134$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 113.

$$2260-904x=\sqrt{7^{2}+\left(-8\right)^{2}}\times 4\sqrt{13}$$

Calculate 7 to the power of 2 and get 49.

$$2260-904x=\sqrt{49+\left(-8\right)^{2}}\times 4\sqrt{13}$$

Calculate -8 to the power of 2 and get 64.

$$2260-904x=\sqrt{49+64}\times 4\sqrt{13}$$

Add 49 and 64 to get 113.

$$2260-904x=\sqrt{113}\times 4\sqrt{13}$$

To multiply \sqrt{113} and \sqrt{13}, multiply the numbers under the square root.

$$2260-904x=\sqrt{1469}\times 4$$

Subtract 2260 from both sides.

$$-904x=\sqrt{1469}\times 4-2260$$

The equation is in standard form.

$$-904x=4\sqrt{1469}-2260$$

Divide both sides by -904.

$$\frac{-904x}{-904}=\frac{4\sqrt{1469}-2260}{-904}$$

Dividing by -904 undoes the multiplication by -904.

$$x=\frac{4\sqrt{1469}-2260}{-904}$$

Divide 4\sqrt{1469}-2260 by -904.

$$x=-\frac{\sqrt{1469}}{226}+\frac{5}{2}$$