1x^2+2x=84

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Solution for 1x^2+2x=84 equation:


Simplifying
1x2 + 2x = 84

Reorder the terms:
2x + 1x2 = 84

Solving
2x + 1x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + 2x + 1x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 2x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 2x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + 2x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 2x + x2 = 0 + 84
2x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
2x + x2 = 84

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 = 84 + 1

Reorder the terms:
1 + 2x + x2 = 84 + 1

Combine like terms: 84 + 1 = 85
1 + 2x + x2 = 85

Factor a perfect square on the left side:
(x + 1)(x + 1) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + 1) equal to 9.219544457 and -9.219544457.

Subproblem 1

x + 1 = 9.219544457 Simplifying x + 1 = 9.219544457 Reorder the terms: 1 + x = 9.219544457 Solving 1 + x = 9.219544457 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 = 9.219544457 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.219544457 + -1 x = 9.219544457 + -1 Combine like terms: 9.219544457 + -1 = 8.219544457 x = 8.219544457 Simplifying x = 8.219544457

Subproblem 2

x + 1 = -9.219544457 Simplifying x + 1 = -9.219544457 Reorder the terms: 1 + x = -9.219544457 Solving 1 + x = -9.219544457 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 = -9.219544457 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.219544457 + -1 x = -9.219544457 + -1 Combine like terms: -9.219544457 + -1 = -10.219544457 x = -10.219544457 Simplifying x = -10.219544457

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.219544457, -10.219544457}

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