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Simplifying 2x2 + -6x + -280 = 0 Reorder the terms: -280 + -6x + 2x2 = 0 Solving -280 + -6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-140 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-140 + -3x + x2)' equal to zero and attempt to solve: Simplifying -140 + -3x + x2 = 0 Solving -140 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -3x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -3x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -3x + x2 = 0 + 140 -3x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -3x + x2 = 140 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 = 140 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 140 + 2.25 Combine like terms: 140 + 2.25 = 142.25 2.25 + -3x + x2 = 142.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (x + -1.5) equal to 11.926860442 and -11.926860442.Subproblem 1
x + -1.5 = 11.926860442 Simplifying x + -1.5 = 11.926860442 Reorder the terms: -1.5 + x = 11.926860442 Solving -1.5 + x = 11.926860442 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 = 11.926860442 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 11.926860442 + 1.5 x = 11.926860442 + 1.5 Combine like terms: 11.926860442 + 1.5 = 13.426860442 x = 13.426860442 Simplifying x = 13.426860442Subproblem 2
x + -1.5 = -11.926860442 Simplifying x + -1.5 = -11.926860442 Reorder the terms: -1.5 + x = -11.926860442 Solving -1.5 + x = -11.926860442 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 = -11.926860442 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -11.926860442 + 1.5 x = -11.926860442 + 1.5 Combine like terms: -11.926860442 + 1.5 = -10.426860442 x = -10.426860442 Simplifying x = -10.426860442Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.426860442, -10.426860442}Solution
x = {13.426860442, -10.426860442}
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