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Simplifying 3x2 + 8x = 420 Reorder the terms: 8x + 3x2 = 420 Solving 8x + 3x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 8x + 3x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -140 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 2.666666667x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 2.666666667x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 2.666666667x + x2 = 0 + 140 2.666666667x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 2.666666667x + x2 = 140 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 = 140 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 140 + 1.777777780 Combine like terms: 140 + 1.777777780 = 141.77777778 1.777777780 + 2.666666667x + x2 = 141.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 141.77777778 Calculate the square root of the right side: 11.9070474 Break this problem into two subproblems by setting (x + 1.333333334) equal to 11.9070474 and -11.9070474.Subproblem 1
x + 1.333333334 = 11.9070474 Simplifying x + 1.333333334 = 11.9070474 Reorder the terms: 1.333333334 + x = 11.9070474 Solving 1.333333334 + x = 11.9070474 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 = 11.9070474 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 11.9070474 + -1.333333334 x = 11.9070474 + -1.333333334 Combine like terms: 11.9070474 + -1.333333334 = 10.573714066 x = 10.573714066 Simplifying x = 10.573714066Subproblem 2
x + 1.333333334 = -11.9070474 Simplifying x + 1.333333334 = -11.9070474 Reorder the terms: 1.333333334 + x = -11.9070474 Solving 1.333333334 + x = -11.9070474 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 = -11.9070474 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -11.9070474 + -1.333333334 x = -11.9070474 + -1.333333334 Combine like terms: -11.9070474 + -1.333333334 = -13.240380734 x = -13.240380734 Simplifying x = -13.240380734Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.573714066, -13.240380734}
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