Solve {x^{2}=9^{2}+6^{2}+7^{2}+4^{2}+3^{2}+3^2+2^2+5^2+2^2

$$\{ x ^ { 2 } = 9 ^ { 2 } + 6 ^ { 2 } + 7 ^ { 2 } + 4 ^ { 2 } + 3 ^ { 2 } + 3 ^ { 2 } + 2 ^ { 2 } + 5 ^ { 2 } + 2 ^ { 2 }$$

Solve for x

$$x=\sqrt{233}\approx 15.264337522$$

$$x=-\sqrt{233}\approx -15.264337522$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$x^{2}=81+6^{2}+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}=81+36+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Add 81 and 36 to get 117.

$$x^{2}=117+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 7 to the power of 2 and get 49.

$$x^{2}=117+49+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Add 117 and 49 to get 166.

$$x^{2}=166+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}=166+16+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Add 166 and 16 to get 182.

$$x^{2}=182+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=182+9+3^{2}+2^{2}+5^{2}+2^{2}$$

Add 182 and 9 to get 191.

$$x^{2}=191+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=191+9+2^{2}+5^{2}+2^{2}$$

Add 191 and 9 to get 200.

$$x^{2}=200+2^{2}+5^{2}+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}=200+4+5^{2}+2^{2}$$

Add 200 and 4 to get 204.

$$x^{2}=204+5^{2}+2^{2}$$

Calculate 5 to the power of 2 and get 25.

$$x^{2}=204+25+2^{2}$$

Add 204 and 25 to get 229.

$$x^{2}=229+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}=229+4$$

Add 229 and 4 to get 233.

$$x^{2}=233$$

Take the square root of both sides of the equation.

$$x=\sqrt{233} x=-\sqrt{233}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$x^{2}=81+6^{2}+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}=81+36+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Add 81 and 36 to get 117.

$$x^{2}=117+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 7 to the power of 2 and get 49.

$$x^{2}=117+49+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Add 117 and 49 to get 166.

$$x^{2}=166+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}=166+16+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Add 166 and 16 to get 182.

$$x^{2}=182+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=182+9+3^{2}+2^{2}+5^{2}+2^{2}$$

Add 182 and 9 to get 191.

$$x^{2}=191+3^{2}+2^{2}+5^{2}+2^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=191+9+2^{2}+5^{2}+2^{2}$$

Add 191 and 9 to get 200.

$$x^{2}=200+2^{2}+5^{2}+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}=200+4+5^{2}+2^{2}$$

Add 200 and 4 to get 204.

$$x^{2}=204+5^{2}+2^{2}$$

Calculate 5 to the power of 2 and get 25.

$$x^{2}=204+25+2^{2}$$

Add 204 and 25 to get 229.

$$x^{2}=229+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}=229+4$$

Add 229 and 4 to get 233.

$$x^{2}=233$$

Subtract 233 from both sides.

$$x^{2}-233=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -233 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-233\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-233\right)}}{2}$$

Multiply -4 times -233.

$$x=\frac{0±\sqrt{932}}{2}$$

Take the square root of 932.

$$x=\frac{0±2\sqrt{233}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{233}}{2} when ± is plus.

$$x=\sqrt{233}$$

Now solve the equation x=\frac{0±2\sqrt{233}}{2} when ± is minus.

$$x=-\sqrt{233}$$

The equation is now solved.

$$x=\sqrt{233} x=-\sqrt{233}$$