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Simplifying 100 = 3x2 + 17x + -20 Reorder the terms: 100 = -20 + 17x + 3x2 Solving 100 = -20 + 17x + 3x2 Solving for variable 'x'. Combine like terms: 100 + 20 = 120 120 + -17x + -3x2 = -20 + 17x + 3x2 + 20 + -17x + -3x2 Reorder the terms: 120 + -17x + -3x2 = -20 + 20 + 17x + -17x + 3x2 + -3x2 Combine like terms: -20 + 20 = 0 120 + -17x + -3x2 = 0 + 17x + -17x + 3x2 + -3x2 120 + -17x + -3x2 = 17x + -17x + 3x2 + -3x2 Combine like terms: 17x + -17x = 0 120 + -17x + -3x2 = 0 + 3x2 + -3x2 120 + -17x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 120 + -17x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -40 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 5.666666667x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 5.666666667x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 5.666666667x + x2 = 0 + 40 5.666666667x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 5.666666667x + x2 = 40 The x term is 5.666666667x. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x + 8.027777782 + x2 = 40 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 40 + 8.027777782 Combine like terms: 40 + 8.027777782 = 48.027777782 8.027777782 + 5.666666667x + x2 = 48.027777782 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 48.027777782 Calculate the square root of the right side: 6.930207629 Break this problem into two subproblems by setting (x + 2.833333334) equal to 6.930207629 and -6.930207629.Subproblem 1
x + 2.833333334 = 6.930207629 Simplifying x + 2.833333334 = 6.930207629 Reorder the terms: 2.833333334 + x = 6.930207629 Solving 2.833333334 + x = 6.930207629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 6.930207629 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 6.930207629 + -2.833333334 x = 6.930207629 + -2.833333334 Combine like terms: 6.930207629 + -2.833333334 = 4.096874295 x = 4.096874295 Simplifying x = 4.096874295Subproblem 2
x + 2.833333334 = -6.930207629 Simplifying x + 2.833333334 = -6.930207629 Reorder the terms: 2.833333334 + x = -6.930207629 Solving 2.833333334 + x = -6.930207629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -6.930207629 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -6.930207629 + -2.833333334 x = -6.930207629 + -2.833333334 Combine like terms: -6.930207629 + -2.833333334 = -9.763540963 x = -9.763540963 Simplifying x = -9.763540963Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.096874295, -9.763540963}
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