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Simplifying 4x2 + 42x + -108 = 0 Reorder the terms: -108 + 42x + 4x2 = 0 Solving -108 + 42x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + 21x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + 21x + 2x2)' equal to zero and attempt to solve: Simplifying -54 + 21x + 2x2 = 0 Solving -54 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27 + 10.5x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + 10.5x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 10.5x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 10.5x + x2 = 0 + 27 10.5x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 10.5x + x2 = 27 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 27 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 27 + 27.5625 Combine like terms: 27 + 27.5625 = 54.5625 27.5625 + 10.5x + x2 = 54.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 54.5625 Calculate the square root of the right side: 7.386643351 Break this problem into two subproblems by setting (x + 5.25) equal to 7.386643351 and -7.386643351.Subproblem 1
x + 5.25 = 7.386643351 Simplifying x + 5.25 = 7.386643351 Reorder the terms: 5.25 + x = 7.386643351 Solving 5.25 + x = 7.386643351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 7.386643351 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 7.386643351 + -5.25 x = 7.386643351 + -5.25 Combine like terms: 7.386643351 + -5.25 = 2.136643351 x = 2.136643351 Simplifying x = 2.136643351Subproblem 2
x + 5.25 = -7.386643351 Simplifying x + 5.25 = -7.386643351 Reorder the terms: 5.25 + x = -7.386643351 Solving 5.25 + x = -7.386643351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -7.386643351 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -7.386643351 + -5.25 x = -7.386643351 + -5.25 Combine like terms: -7.386643351 + -5.25 = -12.636643351 x = -12.636643351 Simplifying x = -12.636643351Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.136643351, -12.636643351}Solution
x = {2.136643351, -12.636643351}
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