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Simplifying 3x2 + 8x + -270 = 0 Reorder the terms: -270 + 8x + 3x2 = 0 Solving -270 + 8x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -90 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 2.666666667x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 2.666666667x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 2.666666667x + x2 = 0 + 90 2.666666667x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 2.666666667x + x2 = 90 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 = 90 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 90 + 1.777777780 Combine like terms: 90 + 1.777777780 = 91.77777778 1.777777780 + 2.666666667x + x2 = 91.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 91.77777778 Calculate the square root of the right side: 9.580071909 Break this problem into two subproblems by setting (x + 1.333333334) equal to 9.580071909 and -9.580071909.Subproblem 1
x + 1.333333334 = 9.580071909 Simplifying x + 1.333333334 = 9.580071909 Reorder the terms: 1.333333334 + x = 9.580071909 Solving 1.333333334 + x = 9.580071909 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 = 9.580071909 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 9.580071909 + -1.333333334 x = 9.580071909 + -1.333333334 Combine like terms: 9.580071909 + -1.333333334 = 8.246738575 x = 8.246738575 Simplifying x = 8.246738575Subproblem 2
x + 1.333333334 = -9.580071909 Simplifying x + 1.333333334 = -9.580071909 Reorder the terms: 1.333333334 + x = -9.580071909 Solving 1.333333334 + x = -9.580071909 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 = -9.580071909 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -9.580071909 + -1.333333334 x = -9.580071909 + -1.333333334 Combine like terms: -9.580071909 + -1.333333334 = -10.913405243 x = -10.913405243 Simplifying x = -10.913405243Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.246738575, -10.913405243}
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