x^2+2*x=70

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Solution for x^2+2*x=70 equation:


Simplifying
x2 + 2x = 70

Reorder the terms:
2x + x2 = 70

Solving
2x + x2 = 70

Solving for variable 'x'.

Reorder the terms:
-70 + 2x + x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-70 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 2x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 2x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 2x + x2 = 0 + 70
2x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
2x + x2 = 70

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 70 + 1

Reorder the terms:
1 + 2x + x2 = 70 + 1

Combine like terms: 70 + 1 = 71
1 + 2x + x2 = 71

Factor a perfect square on the left side:
(x + 1)(x + 1) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 1) equal to 8.426149773 and -8.426149773.

Subproblem 1

x + 1 = 8.426149773 Simplifying x + 1 = 8.426149773 Reorder the terms: 1 + x = 8.426149773 Solving 1 + x = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 8.426149773 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.426149773 + -1 x = 8.426149773 + -1 Combine like terms: 8.426149773 + -1 = 7.426149773 x = 7.426149773 Simplifying x = 7.426149773

Subproblem 2

x + 1 = -8.426149773 Simplifying x + 1 = -8.426149773 Reorder the terms: 1 + x = -8.426149773 Solving 1 + x = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -8.426149773 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.426149773 + -1 x = -8.426149773 + -1 Combine like terms: -8.426149773 + -1 = -9.426149773 x = -9.426149773 Simplifying x = -9.426149773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.426149773, -9.426149773}

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