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Simplifying 5x + 18 = 4x2 + -48x + 144 Reorder the terms: 18 + 5x = 4x2 + -48x + 144 Reorder the terms: 18 + 5x = 144 + -48x + 4x2 Solving 18 + 5x = 144 + -48x + 4x2 Solving for variable 'x'. Reorder the terms: 18 + -144 + 5x + 48x + -4x2 = 144 + -48x + 4x2 + -144 + 48x + -4x2 Combine like terms: 18 + -144 = -126 -126 + 5x + 48x + -4x2 = 144 + -48x + 4x2 + -144 + 48x + -4x2 Combine like terms: 5x + 48x = 53x -126 + 53x + -4x2 = 144 + -48x + 4x2 + -144 + 48x + -4x2 Reorder the terms: -126 + 53x + -4x2 = 144 + -144 + -48x + 48x + 4x2 + -4x2 Combine like terms: 144 + -144 = 0 -126 + 53x + -4x2 = 0 + -48x + 48x + 4x2 + -4x2 -126 + 53x + -4x2 = -48x + 48x + 4x2 + -4x2 Combine like terms: -48x + 48x = 0 -126 + 53x + -4x2 = 0 + 4x2 + -4x2 -126 + 53x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -126 + 53x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 31.5 + -13.25x + x2 = 0 Move the constant term to the right: Add '-31.5' to each side of the equation. 31.5 + -13.25x + -31.5 + x2 = 0 + -31.5 Reorder the terms: 31.5 + -31.5 + -13.25x + x2 = 0 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + -13.25x + x2 = 0 + -31.5 -13.25x + x2 = 0 + -31.5 Combine like terms: 0 + -31.5 = -31.5 -13.25x + x2 = -31.5 The x term is -13.25x. Take half its coefficient (-6.625). Square it (43.890625) and add it to both sides. Add '43.890625' to each side of the equation. -13.25x + 43.890625 + x2 = -31.5 + 43.890625 Reorder the terms: 43.890625 + -13.25x + x2 = -31.5 + 43.890625 Combine like terms: -31.5 + 43.890625 = 12.390625 43.890625 + -13.25x + x2 = 12.390625 Factor a perfect square on the left side: (x + -6.625)(x + -6.625) = 12.390625 Calculate the square root of the right side: 3.52003196 Break this problem into two subproblems by setting (x + -6.625) equal to 3.52003196 and -3.52003196.Subproblem 1
x + -6.625 = 3.52003196 Simplifying x + -6.625 = 3.52003196 Reorder the terms: -6.625 + x = 3.52003196 Solving -6.625 + x = 3.52003196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + x = 3.52003196 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = 3.52003196 + 6.625 x = 3.52003196 + 6.625 Combine like terms: 3.52003196 + 6.625 = 10.14503196 x = 10.14503196 Simplifying x = 10.14503196Subproblem 2
x + -6.625 = -3.52003196 Simplifying x + -6.625 = -3.52003196 Reorder the terms: -6.625 + x = -3.52003196 Solving -6.625 + x = -3.52003196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + x = -3.52003196 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = -3.52003196 + 6.625 x = -3.52003196 + 6.625 Combine like terms: -3.52003196 + 6.625 = 3.10496804 x = 3.10496804 Simplifying x = 3.10496804Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.14503196, 3.10496804}
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