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Simplifying 128 = 3x2 + 53x + 34 Reorder the terms: 128 = 34 + 53x + 3x2 Solving 128 = 34 + 53x + 3x2 Solving for variable 'x'. Combine like terms: 128 + -34 = 94 94 + -53x + -3x2 = 34 + 53x + 3x2 + -34 + -53x + -3x2 Reorder the terms: 94 + -53x + -3x2 = 34 + -34 + 53x + -53x + 3x2 + -3x2 Combine like terms: 34 + -34 = 0 94 + -53x + -3x2 = 0 + 53x + -53x + 3x2 + -3x2 94 + -53x + -3x2 = 53x + -53x + 3x2 + -3x2 Combine like terms: 53x + -53x = 0 94 + -53x + -3x2 = 0 + 3x2 + -3x2 94 + -53x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 94 + -53x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -31.33333333 + 17.66666667x + x2 = 0 Move the constant term to the right: Add '31.33333333' to each side of the equation. -31.33333333 + 17.66666667x + 31.33333333 + x2 = 0 + 31.33333333 Reorder the terms: -31.33333333 + 31.33333333 + 17.66666667x + x2 = 0 + 31.33333333 Combine like terms: -31.33333333 + 31.33333333 = 0.00000000 0.00000000 + 17.66666667x + x2 = 0 + 31.33333333 17.66666667x + x2 = 0 + 31.33333333 Combine like terms: 0 + 31.33333333 = 31.33333333 17.66666667x + x2 = 31.33333333 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 = 31.33333333 + 78.02777781 Reorder the terms: 78.02777781 + 17.66666667x + x2 = 31.33333333 + 78.02777781 Combine like terms: 31.33333333 + 78.02777781 = 109.36111114 78.02777781 + 17.66666667x + x2 = 109.36111114 Factor a perfect square on the left side: (x + 8.833333335)(x + 8.833333335) = 109.36111114 Calculate the square root of the right side: 10.457586296 Break this problem into two subproblems by setting (x + 8.833333335) equal to 10.457586296 and -10.457586296.Subproblem 1
x + 8.833333335 = 10.457586296 Simplifying x + 8.833333335 = 10.457586296 Reorder the terms: 8.833333335 + x = 10.457586296 Solving 8.833333335 + x = 10.457586296 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 = 10.457586296 + -8.833333335 Combine like terms: 8.833333335 + -8.833333335 = 0.000000000 0.000000000 + x = 10.457586296 + -8.833333335 x = 10.457586296 + -8.833333335 Combine like terms: 10.457586296 + -8.833333335 = 1.624252961 x = 1.624252961 Simplifying x = 1.624252961Subproblem 2
x + 8.833333335 = -10.457586296 Simplifying x + 8.833333335 = -10.457586296 Reorder the terms: 8.833333335 + x = -10.457586296 Solving 8.833333335 + x = -10.457586296 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 = -10.457586296 + -8.833333335 Combine like terms: 8.833333335 + -8.833333335 = 0.000000000 0.000000000 + x = -10.457586296 + -8.833333335 x = -10.457586296 + -8.833333335 Combine like terms: -10.457586296 + -8.833333335 = -19.290919631 x = -19.290919631 Simplifying x = -19.290919631Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.624252961, -19.290919631}
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