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Simplifying 2x(x + -62) = 162 Reorder the terms: 2x(-62 + x) = 162 (-62 * 2x + x * 2x) = 162 (-124x + 2x2) = 162 Solving -124x + 2x2 = 162 Solving for variable 'x'. Reorder the terms: -162 + -124x + 2x2 = 162 + -162 Combine like terms: 162 + -162 = 0 -162 + -124x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-81 + -62x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-81 + -62x + x2)' equal to zero and attempt to solve: Simplifying -81 + -62x + x2 = 0 Solving -81 + -62x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -62x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -62x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -62x + x2 = 0 + 81 -62x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -62x + x2 = 81 The x term is -62x. Take half its coefficient (-31). Square it (961) and add it to both sides. Add '961' to each side of the equation. -62x + 961 + x2 = 81 + 961 Reorder the terms: 961 + -62x + x2 = 81 + 961 Combine like terms: 81 + 961 = 1042 961 + -62x + x2 = 1042 Factor a perfect square on the left side: (x + -31)(x + -31) = 1042 Calculate the square root of the right side: 32.280024783 Break this problem into two subproblems by setting (x + -31) equal to 32.280024783 and -32.280024783.Subproblem 1
x + -31 = 32.280024783 Simplifying x + -31 = 32.280024783 Reorder the terms: -31 + x = 32.280024783 Solving -31 + x = 32.280024783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = 32.280024783 + 31 Combine like terms: -31 + 31 = 0 0 + x = 32.280024783 + 31 x = 32.280024783 + 31 Combine like terms: 32.280024783 + 31 = 63.280024783 x = 63.280024783 Simplifying x = 63.280024783Subproblem 2
x + -31 = -32.280024783 Simplifying x + -31 = -32.280024783 Reorder the terms: -31 + x = -32.280024783 Solving -31 + x = -32.280024783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = -32.280024783 + 31 Combine like terms: -31 + 31 = 0 0 + x = -32.280024783 + 31 x = -32.280024783 + 31 Combine like terms: -32.280024783 + 31 = -1.280024783 x = -1.280024783 Simplifying x = -1.280024783Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.280024783, -1.280024783}Solution
x = {63.280024783, -1.280024783}
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