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Simplifying -3(x + 5) * 2x = -15 + -1x Reorder the terms: -3(5 + x) * 2x = -15 + -1x Reorder the terms for easier multiplication: -3 * 2x(5 + x) = -15 + -1x Multiply -3 * 2 -6x(5 + x) = -15 + -1x (5 * -6x + x * -6x) = -15 + -1x (-30x + -6x2) = -15 + -1x Solving -30x + -6x2 = -15 + -1x Solving for variable 'x'. Reorder the terms: 15 + -30x + x + -6x2 = -15 + -1x + 15 + x Combine like terms: -30x + x = -29x 15 + -29x + -6x2 = -15 + -1x + 15 + x Reorder the terms: 15 + -29x + -6x2 = -15 + 15 + -1x + x Combine like terms: -15 + 15 = 0 15 + -29x + -6x2 = 0 + -1x + x 15 + -29x + -6x2 = -1x + x Combine like terms: -1x + x = 0 15 + -29x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.5 + 4.833333333x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 4.833333333x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 4.833333333x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 4.833333333x + x2 = 0 + 2.5 4.833333333x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 4.833333333x + x2 = 2.5 The x term is 4.833333333x. Take half its coefficient (2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. 4.833333333x + 5.840277779 + x2 = 2.5 + 5.840277779 Reorder the terms: 5.840277779 + 4.833333333x + x2 = 2.5 + 5.840277779 Combine like terms: 2.5 + 5.840277779 = 8.340277779 5.840277779 + 4.833333333x + x2 = 8.340277779 Factor a perfect square on the left side: (x + 2.416666667)(x + 2.416666667) = 8.340277779 Calculate the square root of the right side: 2.887953909 Break this problem into two subproblems by setting (x + 2.416666667) equal to 2.887953909 and -2.887953909.Subproblem 1
x + 2.416666667 = 2.887953909 Simplifying x + 2.416666667 = 2.887953909 Reorder the terms: 2.416666667 + x = 2.887953909 Solving 2.416666667 + x = 2.887953909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.416666667' to each side of the equation. 2.416666667 + -2.416666667 + x = 2.887953909 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + x = 2.887953909 + -2.416666667 x = 2.887953909 + -2.416666667 Combine like terms: 2.887953909 + -2.416666667 = 0.471287242 x = 0.471287242 Simplifying x = 0.471287242Subproblem 2
x + 2.416666667 = -2.887953909 Simplifying x + 2.416666667 = -2.887953909 Reorder the terms: 2.416666667 + x = -2.887953909 Solving 2.416666667 + x = -2.887953909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.416666667' to each side of the equation. 2.416666667 + -2.416666667 + x = -2.887953909 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + x = -2.887953909 + -2.416666667 x = -2.887953909 + -2.416666667 Combine like terms: -2.887953909 + -2.416666667 = -5.304620576 x = -5.304620576 Simplifying x = -5.304620576Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.471287242, -5.304620576}
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