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Simplifying (6x + 2)(x + -5) = 5 Reorder the terms: (2 + 6x)(x + -5) = 5 Reorder the terms: (2 + 6x)(-5 + x) = 5 Multiply (2 + 6x) * (-5 + x) (2(-5 + x) + 6x * (-5 + x)) = 5 ((-5 * 2 + x * 2) + 6x * (-5 + x)) = 5 ((-10 + 2x) + 6x * (-5 + x)) = 5 (-10 + 2x + (-5 * 6x + x * 6x)) = 5 (-10 + 2x + (-30x + 6x2)) = 5 Combine like terms: 2x + -30x = -28x (-10 + -28x + 6x2) = 5 Solving -10 + -28x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: -10 + -5 + -28x + 6x2 = 5 + -5 Combine like terms: -10 + -5 = -15 -15 + -28x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -15 + -28x + 6x2 = 0 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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