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Simplifying 4x2 + 6x = 252 Reorder the terms: 6x + 4x2 = 252 Solving 6x + 4x2 = 252 Solving for variable 'x'. Reorder the terms: -252 + 6x + 4x2 = 252 + -252 Combine like terms: 252 + -252 = 0 -252 + 6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-126 + 3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-126 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -126 + 3x + 2x2 = 0 Solving -126 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -63 + 1.5x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 1.5x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 1.5x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 1.5x + x2 = 0 + 63 1.5x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 1.5x + x2 = 63 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 63 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 63 + 0.5625 Combine like terms: 63 + 0.5625 = 63.5625 0.5625 + 1.5x + x2 = 63.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 63.5625 Calculate the square root of the right side: 7.97260936 Break this problem into two subproblems by setting (x + 0.75) equal to 7.97260936 and -7.97260936.Subproblem 1
x + 0.75 = 7.97260936 Simplifying x + 0.75 = 7.97260936 Reorder the terms: 0.75 + x = 7.97260936 Solving 0.75 + x = 7.97260936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 7.97260936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.97260936 + -0.75 x = 7.97260936 + -0.75 Combine like terms: 7.97260936 + -0.75 = 7.22260936 x = 7.22260936 Simplifying x = 7.22260936Subproblem 2
x + 0.75 = -7.97260936 Simplifying x + 0.75 = -7.97260936 Reorder the terms: 0.75 + x = -7.97260936 Solving 0.75 + x = -7.97260936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -7.97260936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.97260936 + -0.75 x = -7.97260936 + -0.75 Combine like terms: -7.97260936 + -0.75 = -8.72260936 x = -8.72260936 Simplifying x = -8.72260936Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.22260936, -8.72260936}Solution
x = {7.22260936, -8.72260936}
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