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Simplifying -1x2 + -105x + -1050 = 0 Reorder the terms: -1050 + -105x + -1x2 = 0 Solving -1050 + -105x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1050 + 105x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1050 + 105x + x2)' equal to zero and attempt to solve: Simplifying 1050 + 105x + x2 = 0 Solving 1050 + 105x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1050' to each side of the equation. 1050 + 105x + -1050 + x2 = 0 + -1050 Reorder the terms: 1050 + -1050 + 105x + x2 = 0 + -1050 Combine like terms: 1050 + -1050 = 0 0 + 105x + x2 = 0 + -1050 105x + x2 = 0 + -1050 Combine like terms: 0 + -1050 = -1050 105x + x2 = -1050 The x term is 105x. Take half its coefficient (52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. 105x + 2756.25 + x2 = -1050 + 2756.25 Reorder the terms: 2756.25 + 105x + x2 = -1050 + 2756.25 Combine like terms: -1050 + 2756.25 = 1706.25 2756.25 + 105x + x2 = 1706.25 Factor a perfect square on the left side: (x + 52.5)(x + 52.5) = 1706.25 Calculate the square root of the right side: 41.306779105 Break this problem into two subproblems by setting (x + 52.5) equal to 41.306779105 and -41.306779105.Subproblem 1
x + 52.5 = 41.306779105 Simplifying x + 52.5 = 41.306779105 Reorder the terms: 52.5 + x = 41.306779105 Solving 52.5 + x = 41.306779105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + x = 41.306779105 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + x = 41.306779105 + -52.5 x = 41.306779105 + -52.5 Combine like terms: 41.306779105 + -52.5 = -11.193220895 x = -11.193220895 Simplifying x = -11.193220895Subproblem 2
x + 52.5 = -41.306779105 Simplifying x + 52.5 = -41.306779105 Reorder the terms: 52.5 + x = -41.306779105 Solving 52.5 + x = -41.306779105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + x = -41.306779105 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + x = -41.306779105 + -52.5 x = -41.306779105 + -52.5 Combine like terms: -41.306779105 + -52.5 = -93.806779105 x = -93.806779105 Simplifying x = -93.806779105Solution
The solution to the problem is based on the solutions from the subproblems. x = {-11.193220895, -93.806779105}Solution
x = {-11.193220895, -93.806779105}
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