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Simplifying (12)(4x2 + 14x + 14) = 9000 Reorder the terms: 12(14 + 14x + 4x2) = 9000 (14 * 12 + 14x * 12 + 4x2 * 12) = 9000 (168 + 168x + 48x2) = 9000 Solving 168 + 168x + 48x2 = 9000 Solving for variable 'x'. Reorder the terms: 168 + -9000 + 168x + 48x2 = 9000 + -9000 Combine like terms: 168 + -9000 = -8832 -8832 + 168x + 48x2 = 9000 + -9000 Combine like terms: 9000 + -9000 = 0 -8832 + 168x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '24'. 24(-368 + 7x + 2x2) = 0 Ignore the factor 24.Subproblem 1
Set the factor '(-368 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -368 + 7x + 2x2 = 0 Solving -368 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -184 + 3.5x + x2 = 0 Move the constant term to the right: Add '184' to each side of the equation. -184 + 3.5x + 184 + x2 = 0 + 184 Reorder the terms: -184 + 184 + 3.5x + x2 = 0 + 184 Combine like terms: -184 + 184 = 0 0 + 3.5x + x2 = 0 + 184 3.5x + x2 = 0 + 184 Combine like terms: 0 + 184 = 184 3.5x + x2 = 184 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 184 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 184 + 3.0625 Combine like terms: 184 + 3.0625 = 187.0625 3.0625 + 3.5x + x2 = 187.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 187.0625 Calculate the square root of the right side: 13.677079367 Break this problem into two subproblems by setting (x + 1.75) equal to 13.677079367 and -13.677079367.Subproblem 1
x + 1.75 = 13.677079367 Simplifying x + 1.75 = 13.677079367 Reorder the terms: 1.75 + x = 13.677079367 Solving 1.75 + x = 13.677079367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 13.677079367 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 13.677079367 + -1.75 x = 13.677079367 + -1.75 Combine like terms: 13.677079367 + -1.75 = 11.927079367 x = 11.927079367 Simplifying x = 11.927079367Subproblem 2
x + 1.75 = -13.677079367 Simplifying x + 1.75 = -13.677079367 Reorder the terms: 1.75 + x = -13.677079367 Solving 1.75 + x = -13.677079367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -13.677079367 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -13.677079367 + -1.75 x = -13.677079367 + -1.75 Combine like terms: -13.677079367 + -1.75 = -15.427079367 x = -15.427079367 Simplifying x = -15.427079367Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.927079367, -15.427079367}Solution
x = {11.927079367, -15.427079367}
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