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Simplifying -3x2 + -48x + 100 = 0 Reorder the terms: 100 + -48x + -3x2 = 0 Solving 100 + -48x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -33.33333333 + 16x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + 16x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + 16x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + 16x + x2 = 0 + 33.33333333 16x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 16x + x2 = 33.33333333 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 33.33333333 + 64 Reorder the terms: 64 + 16x + x2 = 33.33333333 + 64 Combine like terms: 33.33333333 + 64 = 97.33333333 64 + 16x + x2 = 97.33333333 Factor a perfect square on the left side: (x + 8)(x + 8) = 97.33333333 Calculate the square root of the right side: 9.865765724 Break this problem into two subproblems by setting (x + 8) equal to 9.865765724 and -9.865765724.Subproblem 1
x + 8 = 9.865765724 Simplifying x + 8 = 9.865765724 Reorder the terms: 8 + x = 9.865765724 Solving 8 + x = 9.865765724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 9.865765724 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.865765724 + -8 x = 9.865765724 + -8 Combine like terms: 9.865765724 + -8 = 1.865765724 x = 1.865765724 Simplifying x = 1.865765724Subproblem 2
x + 8 = -9.865765724 Simplifying x + 8 = -9.865765724 Reorder the terms: 8 + x = -9.865765724 Solving 8 + x = -9.865765724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -9.865765724 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.865765724 + -8 x = -9.865765724 + -8 Combine like terms: -9.865765724 + -8 = -17.865765724 x = -17.865765724 Simplifying x = -17.865765724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.865765724, -17.865765724}
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