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Simplifying 0 = 2x2 + 2x + -162 Reorder the terms: 0 = -162 + 2x + 2x2 Solving 0 = -162 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 162 = 162 162 + -2x + -2x2 = -162 + 2x + 2x2 + 162 + -2x + -2x2 Reorder the terms: 162 + -2x + -2x2 = -162 + 162 + 2x + -2x + 2x2 + -2x2 Combine like terms: -162 + 162 = 0 162 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 162 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 162 + -2x + -2x2 = 0 + 2x2 + -2x2 162 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 162 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(81 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(81 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 81 + -1x + -1x2 = 0 Solving 81 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + x + x2 = 0 + 81 x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 x + x2 = 81 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 81 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 81 + 0.25 Combine like terms: 81 + 0.25 = 81.25 1.25 + x2 = 81.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + 0.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + 0.5 = 9.013878189 Simplifying x + 0.5 = 9.013878189 Reorder the terms: 0.5 + x = 9.013878189 Solving 0.5 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.013878189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.013878189 + -0.5 x = 9.013878189 + -0.5 Combine like terms: 9.013878189 + -0.5 = 8.513878189 x = 8.513878189 Simplifying x = 8.513878189Subproblem 2
x + 0.5 = -9.013878189 Simplifying x + 0.5 = -9.013878189 Reorder the terms: 0.5 + x = -9.013878189 Solving 0.5 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.013878189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.013878189 + -0.5 x = -9.013878189 + -0.5 Combine like terms: -9.013878189 + -0.5 = -9.513878189 x = -9.513878189 Simplifying x = -9.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.513878189, -9.513878189}Solution
x = {8.513878189, -9.513878189}
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