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Simplifying 2x2 + 2x = 324 Reorder the terms: 2x + 2x2 = 324 Solving 2x + 2x2 = 324 Solving for variable 'x'. Reorder the terms: -324 + 2x + 2x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -324 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-162 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-162 + x + x2)' equal to zero and attempt to solve: Simplifying -162 + x + x2 = 0 Solving -162 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + x + x2 = 0 + 162 x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 x + x2 = 162 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. x + 0.25 + x2 = 162 + 0.25 Reorder the terms: 0.25 + x + x2 = 162 + 0.25 Combine like terms: 162 + 0.25 = 162.25 0.25 + x + x2 = 162.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + 0.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + 0.5 = 12.737739203 Simplifying x + 0.5 = 12.737739203 Reorder the terms: 0.5 + x = 12.737739203 Solving 0.5 + x = 12.737739203 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 = 12.737739203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.737739203 + -0.5 x = 12.737739203 + -0.5 Combine like terms: 12.737739203 + -0.5 = 12.237739203 x = 12.237739203 Simplifying x = 12.237739203Subproblem 2
x + 0.5 = -12.737739203 Simplifying x + 0.5 = -12.737739203 Reorder the terms: 0.5 + x = -12.737739203 Solving 0.5 + x = -12.737739203 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 = -12.737739203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.737739203 + -0.5 x = -12.737739203 + -0.5 Combine like terms: -12.737739203 + -0.5 = -13.237739203 x = -13.237739203 Simplifying x = -13.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.237739203, -13.237739203}Solution
x = {12.237739203, -13.237739203}
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