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Simplifying 4x2 + 18x + -56 = 0 Reorder the terms: -56 + 18x + 4x2 = 0 Solving -56 + 18x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + 9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -28 + 9x + 2x2 = 0 Solving -28 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 4.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 4.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 4.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 4.5x + x2 = 0 + 14 4.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 4.5x + x2 = 14 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 14 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 14 + 5.0625 Combine like terms: 14 + 5.0625 = 19.0625 5.0625 + 4.5x + x2 = 19.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (x + 2.25) equal to 4.366062299 and -4.366062299.Subproblem 1
x + 2.25 = 4.366062299 Simplifying x + 2.25 = 4.366062299 Reorder the terms: 2.25 + x = 4.366062299 Solving 2.25 + x = 4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 4.366062299 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 4.366062299 + -2.25 x = 4.366062299 + -2.25 Combine like terms: 4.366062299 + -2.25 = 2.116062299 x = 2.116062299 Simplifying x = 2.116062299Subproblem 2
x + 2.25 = -4.366062299 Simplifying x + 2.25 = -4.366062299 Reorder the terms: 2.25 + x = -4.366062299 Solving 2.25 + x = -4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -4.366062299 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -4.366062299 + -2.25 x = -4.366062299 + -2.25 Combine like terms: -4.366062299 + -2.25 = -6.616062299 x = -6.616062299 Simplifying x = -6.616062299Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.116062299, -6.616062299}Solution
x = {2.116062299, -6.616062299}
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