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Simplifying 3x2 + 8x = 210 Reorder the terms: 8x + 3x2 = 210 Solving 8x + 3x2 = 210 Solving for variable 'x'. Reorder the terms: -210 + 8x + 3x2 = 210 + -210 Combine like terms: 210 + -210 = 0 -210 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -70 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 2.666666667x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 2.666666667x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 2.666666667x + x2 = 0 + 70 2.666666667x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 2.666666667x + x2 = 70 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 = 70 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 70 + 1.777777780 Combine like terms: 70 + 1.777777780 = 71.77777778 1.777777780 + 2.666666667x + x2 = 71.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 71.77777778 Calculate the square root of the right side: 8.472176685 Break this problem into two subproblems by setting (x + 1.333333334) equal to 8.472176685 and -8.472176685.Subproblem 1
x + 1.333333334 = 8.472176685 Simplifying x + 1.333333334 = 8.472176685 Reorder the terms: 1.333333334 + x = 8.472176685 Solving 1.333333334 + x = 8.472176685 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 = 8.472176685 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 8.472176685 + -1.333333334 x = 8.472176685 + -1.333333334 Combine like terms: 8.472176685 + -1.333333334 = 7.138843351 x = 7.138843351 Simplifying x = 7.138843351Subproblem 2
x + 1.333333334 = -8.472176685 Simplifying x + 1.333333334 = -8.472176685 Reorder the terms: 1.333333334 + x = -8.472176685 Solving 1.333333334 + x = -8.472176685 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 = -8.472176685 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -8.472176685 + -1.333333334 x = -8.472176685 + -1.333333334 Combine like terms: -8.472176685 + -1.333333334 = -9.805510019 x = -9.805510019 Simplifying x = -9.805510019Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.138843351, -9.805510019}
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