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Simplifying 2x2 + 4x + -272 = 0 Reorder the terms: -272 + 4x + 2x2 = 0 Solving -272 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-136 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-136 + 2x + x2)' equal to zero and attempt to solve: Simplifying -136 + 2x + x2 = 0 Solving -136 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + 2x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + 2x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + 2x + x2 = 0 + 136 2x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 2x + x2 = 136 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 = 136 + 1 Reorder the terms: 1 + 2x + x2 = 136 + 1 Combine like terms: 136 + 1 = 137 1 + 2x + x2 = 137 Factor a perfect square on the left side: (x + 1)(x + 1) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (x + 1) equal to 11.704699911 and -11.704699911.Subproblem 1
x + 1 = 11.704699911 Simplifying x + 1 = 11.704699911 Reorder the terms: 1 + x = 11.704699911 Solving 1 + x = 11.704699911 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 = 11.704699911 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.704699911 + -1 x = 11.704699911 + -1 Combine like terms: 11.704699911 + -1 = 10.704699911 x = 10.704699911 Simplifying x = 10.704699911Subproblem 2
x + 1 = -11.704699911 Simplifying x + 1 = -11.704699911 Reorder the terms: 1 + x = -11.704699911 Solving 1 + x = -11.704699911 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 = -11.704699911 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.704699911 + -1 x = -11.704699911 + -1 Combine like terms: -11.704699911 + -1 = -12.704699911 x = -12.704699911 Simplifying x = -12.704699911Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.704699911, -12.704699911}Solution
x = {10.704699911, -12.704699911}
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