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Simplifying -2x2 = 32x + 92 Reorder the terms: -2x2 = 92 + 32x Solving -2x2 = 92 + 32x Solving for variable 'x'. Reorder the terms: -92 + -32x + -2x2 = 92 + 32x + -92 + -32x Reorder the terms: -92 + -32x + -2x2 = 92 + -92 + 32x + -32x Combine like terms: 92 + -92 = 0 -92 + -32x + -2x2 = 0 + 32x + -32x -92 + -32x + -2x2 = 32x + -32x Combine like terms: 32x + -32x = 0 -92 + -32x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(46 + 16x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(46 + 16x + x2)' equal to zero and attempt to solve: Simplifying 46 + 16x + x2 = 0 Solving 46 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + 16x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + 16x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 16x + x2 = 0 + -46 16x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 16x + x2 = -46 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -46 + 64 Reorder the terms: 64 + 16x + x2 = -46 + 64 Combine like terms: -46 + 64 = 18 64 + 16x + x2 = 18 Factor a perfect square on the left side: (x + 8)(x + 8) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 8) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 8 = 4.242640687 Simplifying x + 8 = 4.242640687 Reorder the terms: 8 + x = 4.242640687 Solving 8 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 4.242640687 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.242640687 + -8 x = 4.242640687 + -8 Combine like terms: 4.242640687 + -8 = -3.757359313 x = -3.757359313 Simplifying x = -3.757359313Subproblem 2
x + 8 = -4.242640687 Simplifying x + 8 = -4.242640687 Reorder the terms: 8 + x = -4.242640687 Solving 8 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -4.242640687 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.242640687 + -8 x = -4.242640687 + -8 Combine like terms: -4.242640687 + -8 = -12.242640687 x = -12.242640687 Simplifying x = -12.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.757359313, -12.242640687}Solution
x = {-3.757359313, -12.242640687}
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