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Simplifying -880 = -16x2 + 96x + 1760 Reorder the terms: -880 = 1760 + 96x + -16x2 Solving -880 = 1760 + 96x + -16x2 Solving for variable 'x'. Combine like terms: -880 + -1760 = -2640 -2640 + -96x + 16x2 = 1760 + 96x + -16x2 + -1760 + -96x + 16x2 Reorder the terms: -2640 + -96x + 16x2 = 1760 + -1760 + 96x + -96x + -16x2 + 16x2 Combine like terms: 1760 + -1760 = 0 -2640 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -2640 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -2640 + -96x + 16x2 = 0 + -16x2 + 16x2 -2640 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -2640 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-165 + -6x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-165 + -6x + x2)' equal to zero and attempt to solve: Simplifying -165 + -6x + x2 = 0 Solving -165 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '165' to each side of the equation. -165 + -6x + 165 + x2 = 0 + 165 Reorder the terms: -165 + 165 + -6x + x2 = 0 + 165 Combine like terms: -165 + 165 = 0 0 + -6x + x2 = 0 + 165 -6x + x2 = 0 + 165 Combine like terms: 0 + 165 = 165 -6x + x2 = 165 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 165 + 9 Reorder the terms: 9 + -6x + x2 = 165 + 9 Combine like terms: 165 + 9 = 174 9 + -6x + x2 = 174 Factor a perfect square on the left side: (x + -3)(x + -3) = 174 Calculate the square root of the right side: 13.190905958 Break this problem into two subproblems by setting (x + -3) equal to 13.190905958 and -13.190905958.Subproblem 1
x + -3 = 13.190905958 Simplifying x + -3 = 13.190905958 Reorder the terms: -3 + x = 13.190905958 Solving -3 + x = 13.190905958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 13.190905958 + 3 Combine like terms: -3 + 3 = 0 0 + x = 13.190905958 + 3 x = 13.190905958 + 3 Combine like terms: 13.190905958 + 3 = 16.190905958 x = 16.190905958 Simplifying x = 16.190905958Subproblem 2
x + -3 = -13.190905958 Simplifying x + -3 = -13.190905958 Reorder the terms: -3 + x = -13.190905958 Solving -3 + x = -13.190905958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -13.190905958 + 3 Combine like terms: -3 + 3 = 0 0 + x = -13.190905958 + 3 x = -13.190905958 + 3 Combine like terms: -13.190905958 + 3 = -10.190905958 x = -10.190905958 Simplifying x = -10.190905958Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.190905958, -10.190905958}Solution
x = {16.190905958, -10.190905958}
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