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Simplifying 6x2 + 24x + -560 = 0 Reorder the terms: -560 + 24x + 6x2 = 0 Solving -560 + 24x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-280 + 12x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-280 + 12x + 3x2)' equal to zero and attempt to solve: Simplifying -280 + 12x + 3x2 = 0 Solving -280 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -93.33333333 + 4x + x2 = 0 Move the constant term to the right: Add '93.33333333' to each side of the equation. -93.33333333 + 4x + 93.33333333 + x2 = 0 + 93.33333333 Reorder the terms: -93.33333333 + 93.33333333 + 4x + x2 = 0 + 93.33333333 Combine like terms: -93.33333333 + 93.33333333 = 0.00000000 0.00000000 + 4x + x2 = 0 + 93.33333333 4x + x2 = 0 + 93.33333333 Combine like terms: 0 + 93.33333333 = 93.33333333 4x + x2 = 93.33333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 93.33333333 + 4 Reorder the terms: 4 + 4x + x2 = 93.33333333 + 4 Combine like terms: 93.33333333 + 4 = 97.33333333 4 + 4x + x2 = 97.33333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 97.33333333 Calculate the square root of the right side: 9.865765724 Break this problem into two subproblems by setting (x + 2) equal to 9.865765724 and -9.865765724.Subproblem 1
x + 2 = 9.865765724 Simplifying x + 2 = 9.865765724 Reorder the terms: 2 + x = 9.865765724 Solving 2 + x = 9.865765724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.865765724 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.865765724 + -2 x = 9.865765724 + -2 Combine like terms: 9.865765724 + -2 = 7.865765724 x = 7.865765724 Simplifying x = 7.865765724Subproblem 2
x + 2 = -9.865765724 Simplifying x + 2 = -9.865765724 Reorder the terms: 2 + x = -9.865765724 Solving 2 + x = -9.865765724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.865765724 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.865765724 + -2 x = -9.865765724 + -2 Combine like terms: -9.865765724 + -2 = -11.865765724 x = -11.865765724 Simplifying x = -11.865765724Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.865765724, -11.865765724}Solution
x = {7.865765724, -11.865765724}
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