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Simplifying 3x(x + -6) + -1(10x + -6) = 0 Reorder the terms: 3x(-6 + x) + -1(10x + -6) = 0 (-6 * 3x + x * 3x) + -1(10x + -6) = 0 (-18x + 3x2) + -1(10x + -6) = 0 Reorder the terms: -18x + 3x2 + -1(-6 + 10x) = 0 -18x + 3x2 + (-6 * -1 + 10x * -1) = 0 -18x + 3x2 + (6 + -10x) = 0 Reorder the terms: 6 + -18x + -10x + 3x2 = 0 Combine like terms: -18x + -10x = -28x 6 + -28x + 3x2 = 0 Solving 6 + -28x + 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'. 2 + -9.333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -9.333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -9.333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9.333333333x + x2 = 0 + -2 -9.333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -9.333333333x + x2 = -2 The x term is -9.333333333x. Take half its coefficient (-4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. -9.333333333x + 21.77777778 + x2 = -2 + 21.77777778 Reorder the terms: 21.77777778 + -9.333333333x + x2 = -2 + 21.77777778 Combine like terms: -2 + 21.77777778 = 19.77777778 21.77777778 + -9.333333333x + x2 = 19.77777778 Factor a perfect square on the left side: (x + -4.666666667)(x + -4.666666667) = 19.77777778 Calculate the square root of the right side: 4.447221355 Break this problem into two subproblems by setting (x + -4.666666667) equal to 4.447221355 and -4.447221355.Subproblem 1
x + -4.666666667 = 4.447221355 Simplifying x + -4.666666667 = 4.447221355 Reorder the terms: -4.666666667 + x = 4.447221355 Solving -4.666666667 + x = 4.447221355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = 4.447221355 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = 4.447221355 + 4.666666667 x = 4.447221355 + 4.666666667 Combine like terms: 4.447221355 + 4.666666667 = 9.113888022 x = 9.113888022 Simplifying x = 9.113888022Subproblem 2
x + -4.666666667 = -4.447221355 Simplifying x + -4.666666667 = -4.447221355 Reorder the terms: -4.666666667 + x = -4.447221355 Solving -4.666666667 + x = -4.447221355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = -4.447221355 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = -4.447221355 + 4.666666667 x = -4.447221355 + 4.666666667 Combine like terms: -4.447221355 + 4.666666667 = 0.219445312 x = 0.219445312 Simplifying x = 0.219445312Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.113888022, 0.219445312}
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