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Simplifying x(3x + 8) = 390 Reorder the terms: x(8 + 3x) = 390 (8 * x + 3x * x) = 390 (8x + 3x2) = 390 Solving 8x + 3x2 = 390 Solving for variable 'x'. Reorder the terms: -390 + 8x + 3x2 = 390 + -390 Combine like terms: 390 + -390 = 0 -390 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -130 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 2.666666667x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 2.666666667x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 2.666666667x + x2 = 0 + 130 2.666666667x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 2.666666667x + x2 = 130 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 = 130 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 130 + 1.777777780 Combine like terms: 130 + 1.777777780 = 131.77777778 1.777777780 + 2.666666667x + x2 = 131.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 131.77777778 Calculate the square root of the right side: 11.479450239 Break this problem into two subproblems by setting (x + 1.333333334) equal to 11.479450239 and -11.479450239.Subproblem 1
x + 1.333333334 = 11.479450239 Simplifying x + 1.333333334 = 11.479450239 Reorder the terms: 1.333333334 + x = 11.479450239 Solving 1.333333334 + x = 11.479450239 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 = 11.479450239 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 11.479450239 + -1.333333334 x = 11.479450239 + -1.333333334 Combine like terms: 11.479450239 + -1.333333334 = 10.146116905 x = 10.146116905 Simplifying x = 10.146116905Subproblem 2
x + 1.333333334 = -11.479450239 Simplifying x + 1.333333334 = -11.479450239 Reorder the terms: 1.333333334 + x = -11.479450239 Solving 1.333333334 + x = -11.479450239 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 = -11.479450239 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -11.479450239 + -1.333333334 x = -11.479450239 + -1.333333334 Combine like terms: -11.479450239 + -1.333333334 = -12.812783573 x = -12.812783573 Simplifying x = -12.812783573Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.146116905, -12.812783573}
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