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Simplifying 3x2 + 8x = 1230 Reorder the terms: 8x + 3x2 = 1230 Solving 8x + 3x2 = 1230 Solving for variable 'x'. Reorder the terms: -1230 + 8x + 3x2 = 1230 + -1230 Combine like terms: 1230 + -1230 = 0 -1230 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -410 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '410' to each side of the equation. -410 + 2.666666667x + 410 + x2 = 0 + 410 Reorder the terms: -410 + 410 + 2.666666667x + x2 = 0 + 410 Combine like terms: -410 + 410 = 0 0 + 2.666666667x + x2 = 0 + 410 2.666666667x + x2 = 0 + 410 Combine like terms: 0 + 410 = 410 2.666666667x + x2 = 410 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 = 410 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 410 + 1.777777780 Combine like terms: 410 + 1.777777780 = 411.77777778 1.777777780 + 2.666666667x + x2 = 411.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 411.77777778 Calculate the square root of the right side: 20.29230834 Break this problem into two subproblems by setting (x + 1.333333334) equal to 20.29230834 and -20.29230834.Subproblem 1
x + 1.333333334 = 20.29230834 Simplifying x + 1.333333334 = 20.29230834 Reorder the terms: 1.333333334 + x = 20.29230834 Solving 1.333333334 + x = 20.29230834 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 = 20.29230834 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 20.29230834 + -1.333333334 x = 20.29230834 + -1.333333334 Combine like terms: 20.29230834 + -1.333333334 = 18.958975006 x = 18.958975006 Simplifying x = 18.958975006Subproblem 2
x + 1.333333334 = -20.29230834 Simplifying x + 1.333333334 = -20.29230834 Reorder the terms: 1.333333334 + x = -20.29230834 Solving 1.333333334 + x = -20.29230834 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 = -20.29230834 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -20.29230834 + -1.333333334 x = -20.29230834 + -1.333333334 Combine like terms: -20.29230834 + -1.333333334 = -21.625641674 x = -21.625641674 Simplifying x = -21.625641674Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.958975006, -21.625641674}
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