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Simplifying 3x2 + -53x = -56 Reorder the terms: -53x + 3x2 = -56 Solving -53x + 3x2 = -56 Solving for variable 'x'. Reorder the terms: 56 + -53x + 3x2 = -56 + 56 Combine like terms: -56 + 56 = 0 56 + -53x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 18.66666667 + -17.66666667x + x2 = 0 Move the constant term to the right: Add '-18.66666667' to each side of the equation. 18.66666667 + -17.66666667x + -18.66666667 + x2 = 0 + -18.66666667 Reorder the terms: 18.66666667 + -18.66666667 + -17.66666667x + x2 = 0 + -18.66666667 Combine like terms: 18.66666667 + -18.66666667 = 0.00000000 0.00000000 + -17.66666667x + x2 = 0 + -18.66666667 -17.66666667x + x2 = 0 + -18.66666667 Combine like terms: 0 + -18.66666667 = -18.66666667 -17.66666667x + x2 = -18.66666667 The x term is -17.66666667x. Take half its coefficient (-8.833333335). Square it (78.02777781) and add it to both sides. Add '78.02777781' to each side of the equation. -17.66666667x + 78.02777781 + x2 = -18.66666667 + 78.02777781 Reorder the terms: 78.02777781 + -17.66666667x + x2 = -18.66666667 + 78.02777781 Combine like terms: -18.66666667 + 78.02777781 = 59.36111114 78.02777781 + -17.66666667x + x2 = 59.36111114 Factor a perfect square on the left side: (x + -8.833333335)(x + -8.833333335) = 59.36111114 Calculate the square root of the right side: 7.704616223 Break this problem into two subproblems by setting (x + -8.833333335) equal to 7.704616223 and -7.704616223.Subproblem 1
x + -8.833333335 = 7.704616223 Simplifying x + -8.833333335 = 7.704616223 Reorder the terms: -8.833333335 + x = 7.704616223 Solving -8.833333335 + x = 7.704616223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.833333335' to each side of the equation. -8.833333335 + 8.833333335 + x = 7.704616223 + 8.833333335 Combine like terms: -8.833333335 + 8.833333335 = 0.000000000 0.000000000 + x = 7.704616223 + 8.833333335 x = 7.704616223 + 8.833333335 Combine like terms: 7.704616223 + 8.833333335 = 16.537949558 x = 16.537949558 Simplifying x = 16.537949558Subproblem 2
x + -8.833333335 = -7.704616223 Simplifying x + -8.833333335 = -7.704616223 Reorder the terms: -8.833333335 + x = -7.704616223 Solving -8.833333335 + x = -7.704616223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.833333335' to each side of the equation. -8.833333335 + 8.833333335 + x = -7.704616223 + 8.833333335 Combine like terms: -8.833333335 + 8.833333335 = 0.000000000 0.000000000 + x = -7.704616223 + 8.833333335 x = -7.704616223 + 8.833333335 Combine like terms: -7.704616223 + 8.833333335 = 1.128717112 x = 1.128717112 Simplifying x = 1.128717112Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.537949558, 1.128717112}
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