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Simplifying 2x2 + -6x + -9 = 89 Reorder the terms: -9 + -6x + 2x2 = 89 Solving -9 + -6x + 2x2 = 89 Solving for variable 'x'. Reorder the terms: -9 + -89 + -6x + 2x2 = 89 + -89 Combine like terms: -9 + -89 = -98 -98 + -6x + 2x2 = 89 + -89 Combine like terms: 89 + -89 = 0 -98 + -6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + -3x + x2)' equal to zero and attempt to solve: Simplifying -49 + -3x + x2 = 0 Solving -49 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -3x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -3x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -3x + x2 = 0 + 49 -3x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -3x + x2 = 49 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 49 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 49 + 2.25 Combine like terms: 49 + 2.25 = 51.25 2.25 + -3x + x2 = 51.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -1.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -1.5 = 7.158910532 Simplifying x + -1.5 = 7.158910532 Reorder the terms: -1.5 + x = 7.158910532 Solving -1.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 7.158910532 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.158910532 + 1.5 x = 7.158910532 + 1.5 Combine like terms: 7.158910532 + 1.5 = 8.658910532 x = 8.658910532 Simplifying x = 8.658910532Subproblem 2
x + -1.5 = -7.158910532 Simplifying x + -1.5 = -7.158910532 Reorder the terms: -1.5 + x = -7.158910532 Solving -1.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -7.158910532 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.158910532 + 1.5 x = -7.158910532 + 1.5 Combine like terms: -7.158910532 + 1.5 = -5.658910532 x = -5.658910532 Simplifying x = -5.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.658910532, -5.658910532}Solution
x = {8.658910532, -5.658910532}
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