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Simplifying 3x2 + 8x = 225 Reorder the terms: 8x + 3x2 = 225 Solving 8x + 3x2 = 225 Solving for variable 'x'. Reorder the terms: -225 + 8x + 3x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -75 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 2.666666667x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 2.666666667x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 2.666666667x + x2 = 0 + 75 2.666666667x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 2.666666667x + x2 = 75 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 = 75 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 75 + 1.777777780 Combine like terms: 75 + 1.777777780 = 76.77777778 1.777777780 + 2.666666667x + x2 = 76.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 76.77777778 Calculate the square root of the right side: 8.762292952 Break this problem into two subproblems by setting (x + 1.333333334) equal to 8.762292952 and -8.762292952.Subproblem 1
x + 1.333333334 = 8.762292952 Simplifying x + 1.333333334 = 8.762292952 Reorder the terms: 1.333333334 + x = 8.762292952 Solving 1.333333334 + x = 8.762292952 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 = 8.762292952 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 8.762292952 + -1.333333334 x = 8.762292952 + -1.333333334 Combine like terms: 8.762292952 + -1.333333334 = 7.428959618 x = 7.428959618 Simplifying x = 7.428959618Subproblem 2
x + 1.333333334 = -8.762292952 Simplifying x + 1.333333334 = -8.762292952 Reorder the terms: 1.333333334 + x = -8.762292952 Solving 1.333333334 + x = -8.762292952 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 = -8.762292952 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -8.762292952 + -1.333333334 x = -8.762292952 + -1.333333334 Combine like terms: -8.762292952 + -1.333333334 = -10.095626286 x = -10.095626286 Simplifying x = -10.095626286Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.428959618, -10.095626286}
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