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Simplifying 198 = 3x2 + 8x + -42 Reorder the terms: 198 = -42 + 8x + 3x2 Solving 198 = -42 + 8x + 3x2 Solving for variable 'x'. Combine like terms: 198 + 42 = 240 240 + -8x + -3x2 = -42 + 8x + 3x2 + 42 + -8x + -3x2 Reorder the terms: 240 + -8x + -3x2 = -42 + 42 + 8x + -8x + 3x2 + -3x2 Combine like terms: -42 + 42 = 0 240 + -8x + -3x2 = 0 + 8x + -8x + 3x2 + -3x2 240 + -8x + -3x2 = 8x + -8x + 3x2 + -3x2 Combine like terms: 8x + -8x = 0 240 + -8x + -3x2 = 0 + 3x2 + -3x2 240 + -8x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 240 + -8x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -80 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 2.666666667x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 2.666666667x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 2.666666667x + x2 = 0 + 80 2.666666667x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 2.666666667x + x2 = 80 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 80 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 80 + 1.777777780 Combine like terms: 80 + 1.777777780 = 81.77777778 1.777777780 + 2.666666667x + x2 = 81.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 81.77777778 Calculate the square root of the right side: 9.043106644 Break this problem into two subproblems by setting (x + 1.333333334) equal to 9.043106644 and -9.043106644.Subproblem 1
x + 1.333333334 = 9.043106644 Simplifying x + 1.333333334 = 9.043106644 Reorder the terms: 1.333333334 + x = 9.043106644 Solving 1.333333334 + x = 9.043106644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 9.043106644 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 9.043106644 + -1.333333334 x = 9.043106644 + -1.333333334 Combine like terms: 9.043106644 + -1.333333334 = 7.70977331 x = 7.70977331 Simplifying x = 7.70977331Subproblem 2
x + 1.333333334 = -9.043106644 Simplifying x + 1.333333334 = -9.043106644 Reorder the terms: 1.333333334 + x = -9.043106644 Solving 1.333333334 + x = -9.043106644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -9.043106644 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -9.043106644 + -1.333333334 x = -9.043106644 + -1.333333334 Combine like terms: -9.043106644 + -1.333333334 = -10.376439978 x = -10.376439978 Simplifying x = -10.376439978Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.70977331, -10.376439978}
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