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Simplifying (5 + -1x)(6x + 2) + 5 = 0 Reorder the terms: (5 + -1x)(2 + 6x) + 5 = 0 Multiply (5 + -1x) * (2 + 6x) (5(2 + 6x) + -1x * (2 + 6x)) + 5 = 0 ((2 * 5 + 6x * 5) + -1x * (2 + 6x)) + 5 = 0 ((10 + 30x) + -1x * (2 + 6x)) + 5 = 0 (10 + 30x + (2 * -1x + 6x * -1x)) + 5 = 0 (10 + 30x + (-2x + -6x2)) + 5 = 0 Combine like terms: 30x + -2x = 28x (10 + 28x + -6x2) + 5 = 0 Reorder the terms: 10 + 5 + 28x + -6x2 = 0 Combine like terms: 10 + 5 = 15 15 + 28x + -6x2 = 0 Solving 15 + 28x + -6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.5 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -4.666666667x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -4.666666667x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -4.666666667x + x2 = 0 + 2.5 -4.666666667x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -4.666666667x + x2 = 2.5 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 2.5 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 2.5 + 5.444444448 Combine like terms: 2.5 + 5.444444448 = 7.944444448 5.444444448 + -4.666666667x + x2 = 7.944444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 7.944444448 Calculate the square root of the right side: 2.818589088 Break this problem into two subproblems by setting (x + -2.333333334) equal to 2.818589088 and -2.818589088.Subproblem 1
x + -2.333333334 = 2.818589088 Simplifying x + -2.333333334 = 2.818589088 Reorder the terms: -2.333333334 + x = 2.818589088 Solving -2.333333334 + x = 2.818589088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.818589088 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.818589088 + 2.333333334 x = 2.818589088 + 2.333333334 Combine like terms: 2.818589088 + 2.333333334 = 5.151922422 x = 5.151922422 Simplifying x = 5.151922422Subproblem 2
x + -2.333333334 = -2.818589088 Simplifying x + -2.333333334 = -2.818589088 Reorder the terms: -2.333333334 + x = -2.818589088 Solving -2.333333334 + x = -2.818589088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.818589088 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.818589088 + 2.333333334 x = -2.818589088 + 2.333333334 Combine like terms: -2.818589088 + 2.333333334 = -0.485255754 x = -0.485255754 Simplifying x = -0.485255754Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.151922422, -0.485255754}
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