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Simplifying 5x + 6 = 4x2 + -48x + 144 Reorder the terms: 6 + 5x = 4x2 + -48x + 144 Reorder the terms: 6 + 5x = 144 + -48x + 4x2 Solving 6 + 5x = 144 + -48x + 4x2 Solving for variable 'x'. Reorder the terms: 6 + -144 + 5x + 48x + -4x2 = 144 + -48x + 4x2 + -144 + 48x + -4x2 Combine like terms: 6 + -144 = -138 -138 + 5x + 48x + -4x2 = 144 + -48x + 4x2 + -144 + 48x + -4x2 Combine like terms: 5x + 48x = 53x -138 + 53x + -4x2 = 144 + -48x + 4x2 + -144 + 48x + -4x2 Reorder the terms: -138 + 53x + -4x2 = 144 + -144 + -48x + 48x + 4x2 + -4x2 Combine like terms: 144 + -144 = 0 -138 + 53x + -4x2 = 0 + -48x + 48x + 4x2 + -4x2 -138 + 53x + -4x2 = -48x + 48x + 4x2 + -4x2 Combine like terms: -48x + 48x = 0 -138 + 53x + -4x2 = 0 + 4x2 + -4x2 -138 + 53x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -138 + 53x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 34.5 + -13.25x + x2 = 0 Move the constant term to the right: Add '-34.5' to each side of the equation. 34.5 + -13.25x + -34.5 + x2 = 0 + -34.5 Reorder the terms: 34.5 + -34.5 + -13.25x + x2 = 0 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + -13.25x + x2 = 0 + -34.5 -13.25x + x2 = 0 + -34.5 Combine like terms: 0 + -34.5 = -34.5 -13.25x + x2 = -34.5 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 = -34.5 + 43.890625 Reorder the terms: 43.890625 + -13.25x + x2 = -34.5 + 43.890625 Combine like terms: -34.5 + 43.890625 = 9.390625 43.890625 + -13.25x + x2 = 9.390625 Factor a perfect square on the left side: (x + -6.625)(x + -6.625) = 9.390625 Calculate the square root of the right side: 3.064412668 Break this problem into two subproblems by setting (x + -6.625) equal to 3.064412668 and -3.064412668.Subproblem 1
x + -6.625 = 3.064412668 Simplifying x + -6.625 = 3.064412668 Reorder the terms: -6.625 + x = 3.064412668 Solving -6.625 + x = 3.064412668 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 = 3.064412668 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = 3.064412668 + 6.625 x = 3.064412668 + 6.625 Combine like terms: 3.064412668 + 6.625 = 9.689412668 x = 9.689412668 Simplifying x = 9.689412668Subproblem 2
x + -6.625 = -3.064412668 Simplifying x + -6.625 = -3.064412668 Reorder the terms: -6.625 + x = -3.064412668 Solving -6.625 + x = -3.064412668 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 = -3.064412668 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = -3.064412668 + 6.625 x = -3.064412668 + 6.625 Combine like terms: -3.064412668 + 6.625 = 3.560587332 x = 3.560587332 Simplifying x = 3.560587332Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.689412668, 3.560587332}
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