Solve (2020+2022+2023+2024+2025+2033+2039)div13=xx...y

$$(2020+2022+2023+2024+2025+2033+2039) \div 13=xx...y$$

Solve for x

$$x = \frac{\sqrt{184418}}{13} \approx 33.033782242$$

$$x = -\frac{\sqrt{184418}}{13} \approx -33.033782242$$

Steps by Finding Square Root

Multiply both sides of the equation by 13.

$$2020+2022+2023+2024+2025+2033+2039=13xx$$

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

$$2020+2022+2023+2024+2025+2033+2039=13x^{2}$$

Add 2020 and 2022 to get 4042.

$$4042+2023+2024+2025+2033+2039=13x^{2}$$

Add 4042 and 2023 to get 6065.

$$6065+2024+2025+2033+2039=13x^{2}$$

Add 6065 and 2024 to get 8089.

$$8089+2025+2033+2039=13x^{2}$$

Add 8089 and 2025 to get 10114.

$$10114+2033+2039=13x^{2}$$

Add 10114 and 2033 to get 12147.

$$12147+2039=13x^{2}$$

Add 12147 and 2039 to get 14186.

$$14186=13x^{2}$$

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

$$13x^{2}=14186$$

Divide both sides by 13.

$$x^{2}=\frac{14186}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{184418}}{13} x=-\frac{\sqrt{184418}}{13}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 13.

$$2020+2022+2023+2024+2025+2033+2039=13xx$$

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

$$2020+2022+2023+2024+2025+2033+2039=13x^{2}$$

Add 2020 and 2022 to get 4042.

$$4042+2023+2024+2025+2033+2039=13x^{2}$$

Add 4042 and 2023 to get 6065.

$$6065+2024+2025+2033+2039=13x^{2}$$

Add 6065 and 2024 to get 8089.

$$8089+2025+2033+2039=13x^{2}$$

Add 8089 and 2025 to get 10114.

$$10114+2033+2039=13x^{2}$$

Add 10114 and 2033 to get 12147.

$$12147+2039=13x^{2}$$

Add 12147 and 2039 to get 14186.

$$14186=13x^{2}$$

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

$$13x^{2}=14186$$

Subtract 14186 from both sides.

$$13x^{2}-14186=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 13 for a, 0 for b, and -14186 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13\left(-14186\right)}}{2\times 13}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13\left(-14186\right)}}{2\times 13}$$

Multiply -4 times 13.

$$x=\frac{0±\sqrt{-52\left(-14186\right)}}{2\times 13}$$

Multiply -52 times -14186.

$$x=\frac{0±\sqrt{737672}}{2\times 13}$$

Take the square root of 737672.

$$x=\frac{0±2\sqrt{184418}}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{0±2\sqrt{184418}}{26}$$

Now solve the equation x=\frac{0±2\sqrt{184418}}{26} when ± is plus.

$$x=\frac{\sqrt{184418}}{13}$$

Now solve the equation x=\frac{0±2\sqrt{184418}}{26} when ± is minus.

$$x=-\frac{\sqrt{184418}}{13}$$

The equation is now solved.

$$x=\frac{\sqrt{184418}}{13} x=-\frac{\sqrt{184418}}{13}$$