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Simplifying 2x2 + 2x = 396 Reorder the terms: 2x + 2x2 = 396 Solving 2x + 2x2 = 396 Solving for variable 'x'. Reorder the terms: -396 + 2x + 2x2 = 396 + -396 Combine like terms: 396 + -396 = 0 -396 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-198 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-198 + x + x2)' equal to zero and attempt to solve: Simplifying -198 + x + x2 = 0 Solving -198 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '198' to each side of the equation. -198 + x + 198 + x2 = 0 + 198 Reorder the terms: -198 + 198 + x + x2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + x + x2 = 0 + 198 x + x2 = 0 + 198 Combine like terms: 0 + 198 = 198 x + x2 = 198 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 = 198 + 0.25 Reorder the terms: 0.25 + x + x2 = 198 + 0.25 Combine like terms: 198 + 0.25 = 198.25 0.25 + x + x2 = 198.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (x + 0.5) equal to 14.08012784 and -14.08012784.Subproblem 1
x + 0.5 = 14.08012784 Simplifying x + 0.5 = 14.08012784 Reorder the terms: 0.5 + x = 14.08012784 Solving 0.5 + x = 14.08012784 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 = 14.08012784 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.08012784 + -0.5 x = 14.08012784 + -0.5 Combine like terms: 14.08012784 + -0.5 = 13.58012784 x = 13.58012784 Simplifying x = 13.58012784Subproblem 2
x + 0.5 = -14.08012784 Simplifying x + 0.5 = -14.08012784 Reorder the terms: 0.5 + x = -14.08012784 Solving 0.5 + x = -14.08012784 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 = -14.08012784 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.08012784 + -0.5 x = -14.08012784 + -0.5 Combine like terms: -14.08012784 + -0.5 = -14.58012784 x = -14.58012784 Simplifying x = -14.58012784Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.58012784, -14.58012784}Solution
x = {13.58012784, -14.58012784}
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