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Simplifying 3x2 + -8x = 39 Reorder the terms: -8x + 3x2 = 39 Solving -8x + 3x2 = 39 Solving for variable 'x'. Reorder the terms: -39 + -8x + 3x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -2.666666667x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -2.666666667x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2.666666667x + x2 = 0 + 13 -2.666666667x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -2.666666667x + x2 = 13 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 = 13 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 13 + 1.777777780 Combine like terms: 13 + 1.777777780 = 14.77777778 1.777777780 + -2.666666667x + x2 = 14.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 14.77777778 Calculate the square root of the right side: 3.844187532 Break this problem into two subproblems by setting (x + -1.333333334) equal to 3.844187532 and -3.844187532.Subproblem 1
x + -1.333333334 = 3.844187532 Simplifying x + -1.333333334 = 3.844187532 Reorder the terms: -1.333333334 + x = 3.844187532 Solving -1.333333334 + x = 3.844187532 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 = 3.844187532 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 3.844187532 + 1.333333334 x = 3.844187532 + 1.333333334 Combine like terms: 3.844187532 + 1.333333334 = 5.177520866 x = 5.177520866 Simplifying x = 5.177520866Subproblem 2
x + -1.333333334 = -3.844187532 Simplifying x + -1.333333334 = -3.844187532 Reorder the terms: -1.333333334 + x = -3.844187532 Solving -1.333333334 + x = -3.844187532 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 = -3.844187532 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -3.844187532 + 1.333333334 x = -3.844187532 + 1.333333334 Combine like terms: -3.844187532 + 1.333333334 = -2.510854198 x = -2.510854198 Simplifying x = -2.510854198Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.177520866, -2.510854198}
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