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Simplifying 75x + -3x2 + -16x + 125 = 0 Reorder the terms: 125 + 75x + -16x + -3x2 = 0 Combine like terms: 75x + -16x = 59x 125 + 59x + -3x2 = 0 Solving 125 + 59x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -41.66666667 + -19.66666667x + x2 = 0 Move the constant term to the right: Add '41.66666667' to each side of the equation. -41.66666667 + -19.66666667x + 41.66666667 + x2 = 0 + 41.66666667 Reorder the terms: -41.66666667 + 41.66666667 + -19.66666667x + x2 = 0 + 41.66666667 Combine like terms: -41.66666667 + 41.66666667 = 0.00000000 0.00000000 + -19.66666667x + x2 = 0 + 41.66666667 -19.66666667x + x2 = 0 + 41.66666667 Combine like terms: 0 + 41.66666667 = 41.66666667 -19.66666667x + x2 = 41.66666667 The x term is -19.66666667x. Take half its coefficient (-9.833333335). Square it (96.69444448) and add it to both sides. Add '96.69444448' to each side of the equation. -19.66666667x + 96.69444448 + x2 = 41.66666667 + 96.69444448 Reorder the terms: 96.69444448 + -19.66666667x + x2 = 41.66666667 + 96.69444448 Combine like terms: 41.66666667 + 96.69444448 = 138.36111115 96.69444448 + -19.66666667x + x2 = 138.36111115 Factor a perfect square on the left side: (x + -9.833333335)(x + -9.833333335) = 138.36111115 Calculate the square root of the right side: 11.762699994 Break this problem into two subproblems by setting (x + -9.833333335) equal to 11.762699994 and -11.762699994.Subproblem 1
x + -9.833333335 = 11.762699994 Simplifying x + -9.833333335 = 11.762699994 Reorder the terms: -9.833333335 + x = 11.762699994 Solving -9.833333335 + x = 11.762699994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.833333335' to each side of the equation. -9.833333335 + 9.833333335 + x = 11.762699994 + 9.833333335 Combine like terms: -9.833333335 + 9.833333335 = 0.000000000 0.000000000 + x = 11.762699994 + 9.833333335 x = 11.762699994 + 9.833333335 Combine like terms: 11.762699994 + 9.833333335 = 21.596033329 x = 21.596033329 Simplifying x = 21.596033329Subproblem 2
x + -9.833333335 = -11.762699994 Simplifying x + -9.833333335 = -11.762699994 Reorder the terms: -9.833333335 + x = -11.762699994 Solving -9.833333335 + x = -11.762699994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.833333335' to each side of the equation. -9.833333335 + 9.833333335 + x = -11.762699994 + 9.833333335 Combine like terms: -9.833333335 + 9.833333335 = 0.000000000 0.000000000 + x = -11.762699994 + 9.833333335 x = -11.762699994 + 9.833333335 Combine like terms: -11.762699994 + 9.833333335 = -1.929366659 x = -1.929366659 Simplifying x = -1.929366659Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.596033329, -1.929366659}
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