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Simplifying 2x2 + 4x = 112 Reorder the terms: 4x + 2x2 = 112 Solving 4x + 2x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + 4x + 2x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-56 + 2x + x2)' equal to zero and attempt to solve: Simplifying -56 + 2x + x2 = 0 Solving -56 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 2x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 2x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 2x + x2 = 0 + 56 2x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 2x + x2 = 56 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 = 56 + 1 Reorder the terms: 1 + 2x + x2 = 56 + 1 Combine like terms: 56 + 1 = 57 1 + 2x + x2 = 57 Factor a perfect square on the left side: (x + 1)(x + 1) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + 1) equal to 7.549834435 and -7.549834435.Subproblem 1
x + 1 = 7.549834435 Simplifying x + 1 = 7.549834435 Reorder the terms: 1 + x = 7.549834435 Solving 1 + x = 7.549834435 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 = 7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.549834435 + -1 x = 7.549834435 + -1 Combine like terms: 7.549834435 + -1 = 6.549834435 x = 6.549834435 Simplifying x = 6.549834435Subproblem 2
x + 1 = -7.549834435 Simplifying x + 1 = -7.549834435 Reorder the terms: 1 + x = -7.549834435 Solving 1 + x = -7.549834435 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 = -7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.549834435 + -1 x = -7.549834435 + -1 Combine like terms: -7.549834435 + -1 = -8.549834435 x = -8.549834435 Simplifying x = -8.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.549834435, -8.549834435}Solution
x = {6.549834435, -8.549834435}
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