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Simplifying -3x(x + 9) + 10x = -34 Reorder the terms: -3x(9 + x) + 10x = -34 (9 * -3x + x * -3x) + 10x = -34 (-27x + -3x2) + 10x = -34 Reorder the terms: -27x + 10x + -3x2 = -34 Combine like terms: -27x + 10x = -17x -17x + -3x2 = -34 Solving -17x + -3x2 = -34 Solving for variable 'x'. Reorder the terms: 34 + -17x + -3x2 = -34 + 34 Combine like terms: -34 + 34 = 0 34 + -17x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -11.33333333 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '11.33333333' to each side of the equation. -11.33333333 + 5.666666667x + 11.33333333 + x2 = 0 + 11.33333333 Reorder the terms: -11.33333333 + 11.33333333 + 5.666666667x + x2 = 0 + 11.33333333 Combine like terms: -11.33333333 + 11.33333333 = 0.00000000 0.00000000 + 5.666666667x + x2 = 0 + 11.33333333 5.666666667x + x2 = 0 + 11.33333333 Combine like terms: 0 + 11.33333333 = 11.33333333 5.666666667x + x2 = 11.33333333 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 = 11.33333333 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 11.33333333 + 8.027777782 Combine like terms: 11.33333333 + 8.027777782 = 19.361111112 8.027777782 + 5.666666667x + x2 = 19.361111112 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 19.361111112 Calculate the square root of the right side: 4.400126261 Break this problem into two subproblems by setting (x + 2.833333334) equal to 4.400126261 and -4.400126261.Subproblem 1
x + 2.833333334 = 4.400126261 Simplifying x + 2.833333334 = 4.400126261 Reorder the terms: 2.833333334 + x = 4.400126261 Solving 2.833333334 + x = 4.400126261 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 = 4.400126261 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 4.400126261 + -2.833333334 x = 4.400126261 + -2.833333334 Combine like terms: 4.400126261 + -2.833333334 = 1.566792927 x = 1.566792927 Simplifying x = 1.566792927Subproblem 2
x + 2.833333334 = -4.400126261 Simplifying x + 2.833333334 = -4.400126261 Reorder the terms: 2.833333334 + x = -4.400126261 Solving 2.833333334 + x = -4.400126261 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 = -4.400126261 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -4.400126261 + -2.833333334 x = -4.400126261 + -2.833333334 Combine like terms: -4.400126261 + -2.833333334 = -7.233459595 x = -7.233459595 Simplifying x = -7.233459595Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.566792927, -7.233459595}
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