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Simplifying 2x2 + 4x + -148 = 0 Reorder the terms: -148 + 4x + 2x2 = 0 Solving -148 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-74 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-74 + 2x + x2)' equal to zero and attempt to solve: Simplifying -74 + 2x + x2 = 0 Solving -74 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 2x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + 2x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 2x + x2 = 0 + 74 2x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 2x + x2 = 74 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 = 74 + 1 Reorder the terms: 1 + 2x + x2 = 74 + 1 Combine like terms: 74 + 1 = 75 1 + 2x + x2 = 75 Factor a perfect square on the left side: (x + 1)(x + 1) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + 1) equal to 8.660254038 and -8.660254038.Subproblem 1
x + 1 = 8.660254038 Simplifying x + 1 = 8.660254038 Reorder the terms: 1 + x = 8.660254038 Solving 1 + x = 8.660254038 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 = 8.660254038 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.660254038 + -1 x = 8.660254038 + -1 Combine like terms: 8.660254038 + -1 = 7.660254038 x = 7.660254038 Simplifying x = 7.660254038Subproblem 2
x + 1 = -8.660254038 Simplifying x + 1 = -8.660254038 Reorder the terms: 1 + x = -8.660254038 Solving 1 + x = -8.660254038 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 = -8.660254038 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.660254038 + -1 x = -8.660254038 + -1 Combine like terms: -8.660254038 + -1 = -9.660254038 x = -9.660254038 Simplifying x = -9.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.660254038, -9.660254038}Solution
x = {7.660254038, -9.660254038}
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