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Simplifying 2x2 + 8x + -160 = 100 Reorder the terms: -160 + 8x + 2x2 = 100 Solving -160 + 8x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: -160 + -100 + 8x + 2x2 = 100 + -100 Combine like terms: -160 + -100 = -260 -260 + 8x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -260 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-130 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-130 + 4x + x2)' equal to zero and attempt to solve: Simplifying -130 + 4x + x2 = 0 Solving -130 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 4x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 4x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 4x + x2 = 0 + 130 4x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 4x + x2 = 130 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 = 130 + 4 Reorder the terms: 4 + 4x + x2 = 130 + 4 Combine like terms: 130 + 4 = 134 4 + 4x + x2 = 134 Factor a perfect square on the left side: (x + 2)(x + 2) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + 2) equal to 11.575836903 and -11.575836903.Subproblem 1
x + 2 = 11.575836903 Simplifying x + 2 = 11.575836903 Reorder the terms: 2 + x = 11.575836903 Solving 2 + x = 11.575836903 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 = 11.575836903 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.575836903 + -2 x = 11.575836903 + -2 Combine like terms: 11.575836903 + -2 = 9.575836903 x = 9.575836903 Simplifying x = 9.575836903Subproblem 2
x + 2 = -11.575836903 Simplifying x + 2 = -11.575836903 Reorder the terms: 2 + x = -11.575836903 Solving 2 + x = -11.575836903 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 = -11.575836903 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.575836903 + -2 x = -11.575836903 + -2 Combine like terms: -11.575836903 + -2 = -13.575836903 x = -13.575836903 Simplifying x = -13.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.575836903, -13.575836903}Solution
x = {9.575836903, -13.575836903}
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