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Simplifying 110 = 2x2 + 32x Reorder the terms: 110 = 32x + 2x2 Solving 110 = 32x + 2x2 Solving for variable 'x'. Reorder the terms: 110 + -32x + -2x2 = 32x + -32x + 2x2 + -2x2 Combine like terms: 32x + -32x = 0 110 + -32x + -2x2 = 0 + 2x2 + -2x2 110 + -32x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 110 + -32x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(55 + -16x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + -16x + -1x2)' equal to zero and attempt to solve: Simplifying 55 + -16x + -1x2 = 0 Solving 55 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -55 + 16x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + 16x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 16x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 16x + x2 = 0 + 55 16x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 16x + x2 = 55 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 = 55 + 64 Reorder the terms: 64 + 16x + x2 = 55 + 64 Combine like terms: 55 + 64 = 119 64 + 16x + x2 = 119 Factor a perfect square on the left side: (x + 8)(x + 8) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + 8) equal to 10.908712115 and -10.908712115.Subproblem 1
x + 8 = 10.908712115 Simplifying x + 8 = 10.908712115 Reorder the terms: 8 + x = 10.908712115 Solving 8 + x = 10.908712115 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 = 10.908712115 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.908712115 + -8 x = 10.908712115 + -8 Combine like terms: 10.908712115 + -8 = 2.908712115 x = 2.908712115 Simplifying x = 2.908712115Subproblem 2
x + 8 = -10.908712115 Simplifying x + 8 = -10.908712115 Reorder the terms: 8 + x = -10.908712115 Solving 8 + x = -10.908712115 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 = -10.908712115 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.908712115 + -8 x = -10.908712115 + -8 Combine like terms: -10.908712115 + -8 = -18.908712115 x = -18.908712115 Simplifying x = -18.908712115Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.908712115, -18.908712115}Solution
x = {2.908712115, -18.908712115}
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