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Simplifying 9x2 + -51x + -130 = 0 Reorder the terms: -130 + -51x + 9x2 = 0 Solving -130 + -51x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -14.44444444 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '14.44444444' to each side of the equation. -14.44444444 + -5.666666667x + 14.44444444 + x2 = 0 + 14.44444444 Reorder the terms: -14.44444444 + 14.44444444 + -5.666666667x + x2 = 0 + 14.44444444 Combine like terms: -14.44444444 + 14.44444444 = 0.00000000 0.00000000 + -5.666666667x + x2 = 0 + 14.44444444 -5.666666667x + x2 = 0 + 14.44444444 Combine like terms: 0 + 14.44444444 = 14.44444444 -5.666666667x + x2 = 14.44444444 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = 14.44444444 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 14.44444444 + 8.027777782 Combine like terms: 14.44444444 + 8.027777782 = 22.472222222 8.027777782 + -5.666666667x + x2 = 22.472222222 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 22.472222222 Calculate the square root of the right side: 4.740487551 Break this problem into two subproblems by setting (x + -2.833333334) equal to 4.740487551 and -4.740487551.Subproblem 1
x + -2.833333334 = 4.740487551 Simplifying x + -2.833333334 = 4.740487551 Reorder the terms: -2.833333334 + x = 4.740487551 Solving -2.833333334 + x = 4.740487551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 4.740487551 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 4.740487551 + 2.833333334 x = 4.740487551 + 2.833333334 Combine like terms: 4.740487551 + 2.833333334 = 7.573820885 x = 7.573820885 Simplifying x = 7.573820885Subproblem 2
x + -2.833333334 = -4.740487551 Simplifying x + -2.833333334 = -4.740487551 Reorder the terms: -2.833333334 + x = -4.740487551 Solving -2.833333334 + x = -4.740487551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -4.740487551 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -4.740487551 + 2.833333334 x = -4.740487551 + 2.833333334 Combine like terms: -4.740487551 + 2.833333334 = -1.907154217 x = -1.907154217 Simplifying x = -1.907154217Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.573820885, -1.907154217}
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