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Simplifying 0 = 4x2 + 46x + -114 Reorder the terms: 0 = -114 + 46x + 4x2 Solving 0 = -114 + 46x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 114 = 114 114 + -46x + -4x2 = -114 + 46x + 4x2 + 114 + -46x + -4x2 Reorder the terms: 114 + -46x + -4x2 = -114 + 114 + 46x + -46x + 4x2 + -4x2 Combine like terms: -114 + 114 = 0 114 + -46x + -4x2 = 0 + 46x + -46x + 4x2 + -4x2 114 + -46x + -4x2 = 46x + -46x + 4x2 + -4x2 Combine like terms: 46x + -46x = 0 114 + -46x + -4x2 = 0 + 4x2 + -4x2 114 + -46x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 114 + -46x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(57 + -23x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(57 + -23x + -2x2)' equal to zero and attempt to solve: Simplifying 57 + -23x + -2x2 = 0 Solving 57 + -23x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -28.5 + 11.5x + x2 = 0 Move the constant term to the right: Add '28.5' to each side of the equation. -28.5 + 11.5x + 28.5 + x2 = 0 + 28.5 Reorder the terms: -28.5 + 28.5 + 11.5x + x2 = 0 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + 11.5x + x2 = 0 + 28.5 11.5x + x2 = 0 + 28.5 Combine like terms: 0 + 28.5 = 28.5 11.5x + x2 = 28.5 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = 28.5 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = 28.5 + 33.0625 Combine like terms: 28.5 + 33.0625 = 61.5625 33.0625 + 11.5x + x2 = 61.5625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 61.5625 Calculate the square root of the right side: 7.846177413 Break this problem into two subproblems by setting (x + 5.75) equal to 7.846177413 and -7.846177413.Subproblem 1
x + 5.75 = 7.846177413 Simplifying x + 5.75 = 7.846177413 Reorder the terms: 5.75 + x = 7.846177413 Solving 5.75 + x = 7.846177413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 7.846177413 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 7.846177413 + -5.75 x = 7.846177413 + -5.75 Combine like terms: 7.846177413 + -5.75 = 2.096177413 x = 2.096177413 Simplifying x = 2.096177413Subproblem 2
x + 5.75 = -7.846177413 Simplifying x + 5.75 = -7.846177413 Reorder the terms: 5.75 + x = -7.846177413 Solving 5.75 + x = -7.846177413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -7.846177413 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -7.846177413 + -5.75 x = -7.846177413 + -5.75 Combine like terms: -7.846177413 + -5.75 = -13.596177413 x = -13.596177413 Simplifying x = -13.596177413Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.096177413, -13.596177413}Solution
x = {2.096177413, -13.596177413}
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