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Simplifying 2(x + 2 * 5 + 5x + x * x + 2) = 236 Multiply 2 * 5 2(x + 10 + 5x + x * x + 2) = 236 Multiply x * x 2(x + 10 + 5x + x2 + 2) = 236 Reorder the terms: 2(10 + 2 + x + 5x + x2) = 236 Combine like terms: 10 + 2 = 12 2(12 + x + 5x + x2) = 236 Combine like terms: x + 5x = 6x 2(12 + 6x + x2) = 236 (12 * 2 + 6x * 2 + x2 * 2) = 236 (24 + 12x + 2x2) = 236 Solving 24 + 12x + 2x2 = 236 Solving for variable 'x'. Reorder the terms: 24 + -236 + 12x + 2x2 = 236 + -236 Combine like terms: 24 + -236 = -212 -212 + 12x + 2x2 = 236 + -236 Combine like terms: 236 + -236 = 0 -212 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-106 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-106 + 6x + x2)' equal to zero and attempt to solve: Simplifying -106 + 6x + x2 = 0 Solving -106 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '106' to each side of the equation. -106 + 6x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + 6x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + 6x + x2 = 0 + 106 6x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 6x + x2 = 106 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 106 + 9 Reorder the terms: 9 + 6x + x2 = 106 + 9 Combine like terms: 106 + 9 = 115 9 + 6x + x2 = 115 Factor a perfect square on the left side: (x + 3)(x + 3) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + 3) equal to 10.723805295 and -10.723805295.Subproblem 1
x + 3 = 10.723805295 Simplifying x + 3 = 10.723805295 Reorder the terms: 3 + x = 10.723805295 Solving 3 + x = 10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 10.723805295 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.723805295 + -3 x = 10.723805295 + -3 Combine like terms: 10.723805295 + -3 = 7.723805295 x = 7.723805295 Simplifying x = 7.723805295Subproblem 2
x + 3 = -10.723805295 Simplifying x + 3 = -10.723805295 Reorder the terms: 3 + x = -10.723805295 Solving 3 + x = -10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -10.723805295 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.723805295 + -3 x = -10.723805295 + -3 Combine like terms: -10.723805295 + -3 = -13.723805295 x = -13.723805295 Simplifying x = -13.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.723805295, -13.723805295}Solution
x = {7.723805295, -13.723805295}
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