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Simplifying (x2 + 2x + -16)(2) = 1150 Reorder the terms: (-16 + 2x + x2)(2) = 1150 Reorder the terms for easier multiplication: 2(-16 + 2x + x2) = 1150 (-16 * 2 + 2x * 2 + x2 * 2) = 1150 (-32 + 4x + 2x2) = 1150 Solving -32 + 4x + 2x2 = 1150 Solving for variable 'x'. Reorder the terms: -32 + -1150 + 4x + 2x2 = 1150 + -1150 Combine like terms: -32 + -1150 = -1182 -1182 + 4x + 2x2 = 1150 + -1150 Combine like terms: 1150 + -1150 = 0 -1182 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-591 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-591 + 2x + x2)' equal to zero and attempt to solve: Simplifying -591 + 2x + x2 = 0 Solving -591 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '591' to each side of the equation. -591 + 2x + 591 + x2 = 0 + 591 Reorder the terms: -591 + 591 + 2x + x2 = 0 + 591 Combine like terms: -591 + 591 = 0 0 + 2x + x2 = 0 + 591 2x + x2 = 0 + 591 Combine like terms: 0 + 591 = 591 2x + x2 = 591 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 = 591 + 1 Reorder the terms: 1 + 2x + x2 = 591 + 1 Combine like terms: 591 + 1 = 592 1 + 2x + x2 = 592 Factor a perfect square on the left side: (x + 1)(x + 1) = 592 Calculate the square root of the right side: 24.331050121 Break this problem into two subproblems by setting (x + 1) equal to 24.331050121 and -24.331050121.Subproblem 1
x + 1 = 24.331050121 Simplifying x + 1 = 24.331050121 Reorder the terms: 1 + x = 24.331050121 Solving 1 + x = 24.331050121 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 = 24.331050121 + -1 Combine like terms: 1 + -1 = 0 0 + x = 24.331050121 + -1 x = 24.331050121 + -1 Combine like terms: 24.331050121 + -1 = 23.331050121 x = 23.331050121 Simplifying x = 23.331050121Subproblem 2
x + 1 = -24.331050121 Simplifying x + 1 = -24.331050121 Reorder the terms: 1 + x = -24.331050121 Solving 1 + x = -24.331050121 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 = -24.331050121 + -1 Combine like terms: 1 + -1 = 0 0 + x = -24.331050121 + -1 x = -24.331050121 + -1 Combine like terms: -24.331050121 + -1 = -25.331050121 x = -25.331050121 Simplifying x = -25.331050121Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.331050121, -25.331050121}Solution
x = {23.331050121, -25.331050121}
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