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Simplifying 3x2 + 8x + -11 = 13 Reorder the terms: -11 + 8x + 3x2 = 13 Solving -11 + 8x + 3x2 = 13 Solving for variable 'x'. Reorder the terms: -11 + -13 + 8x + 3x2 = 13 + -13 Combine like terms: -11 + -13 = -24 -24 + 8x + 3x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -24 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2.666666667x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 2.666666667x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2.666666667x + x2 = 0 + 8 2.666666667x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 2.666666667x + x2 = 8 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 = 8 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 8 + 1.777777780 Combine like terms: 8 + 1.777777780 = 9.77777778 1.777777780 + 2.666666667x + x2 = 9.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 9.77777778 Calculate the square root of the right side: 3.12694384 Break this problem into two subproblems by setting (x + 1.333333334) equal to 3.12694384 and -3.12694384.Subproblem 1
x + 1.333333334 = 3.12694384 Simplifying x + 1.333333334 = 3.12694384 Reorder the terms: 1.333333334 + x = 3.12694384 Solving 1.333333334 + x = 3.12694384 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 = 3.12694384 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 3.12694384 + -1.333333334 x = 3.12694384 + -1.333333334 Combine like terms: 3.12694384 + -1.333333334 = 1.793610506 x = 1.793610506 Simplifying x = 1.793610506Subproblem 2
x + 1.333333334 = -3.12694384 Simplifying x + 1.333333334 = -3.12694384 Reorder the terms: 1.333333334 + x = -3.12694384 Solving 1.333333334 + x = -3.12694384 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 = -3.12694384 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -3.12694384 + -1.333333334 x = -3.12694384 + -1.333333334 Combine like terms: -3.12694384 + -1.333333334 = -4.460277174 x = -4.460277174 Simplifying x = -4.460277174Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.793610506, -4.460277174}
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