2x^2+8x-170=0

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Solution for 2x^2+8x-170=0 equation:


Simplifying
2x2 + 8x + -170 = 0

Reorder the terms:
-170 + 8x + 2x2 = 0

Solving
-170 + 8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-85 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-85 + 4x + x2)' equal to zero and attempt to solve: Simplifying -85 + 4x + x2 = 0 Solving -85 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 4x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 4x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 4x + x2 = 0 + 85 4x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 4x + x2 = 85 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 85 + 4 Reorder the terms: 4 + 4x + x2 = 85 + 4 Combine like terms: 85 + 4 = 89 4 + 4x + x2 = 89 Factor a perfect square on the left side: (x + 2)(x + 2) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 2) equal to 9.433981132 and -9.433981132.

Subproblem 1

x + 2 = 9.433981132 Simplifying x + 2 = 9.433981132 Reorder the terms: 2 + x = 9.433981132 Solving 2 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.433981132 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.433981132 + -2 x = 9.433981132 + -2 Combine like terms: 9.433981132 + -2 = 7.433981132 x = 7.433981132 Simplifying x = 7.433981132

Subproblem 2

x + 2 = -9.433981132 Simplifying x + 2 = -9.433981132 Reorder the terms: 2 + x = -9.433981132 Solving 2 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.433981132 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.433981132 + -2 x = -9.433981132 + -2 Combine like terms: -9.433981132 + -2 = -11.433981132 x = -11.433981132 Simplifying x = -11.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.433981132, -11.433981132}

Solution

x = {7.433981132, -11.433981132}

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