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Simplifying (3x + -2)(x + 5) = 5 Reorder the terms: (-2 + 3x)(x + 5) = 5 Reorder the terms: (-2 + 3x)(5 + x) = 5 Multiply (-2 + 3x) * (5 + x) (-2(5 + x) + 3x * (5 + x)) = 5 ((5 * -2 + x * -2) + 3x * (5 + x)) = 5 ((-10 + -2x) + 3x * (5 + x)) = 5 (-10 + -2x + (5 * 3x + x * 3x)) = 5 (-10 + -2x + (15x + 3x2)) = 5 Combine like terms: -2x + 15x = 13x (-10 + 13x + 3x2) = 5 Solving -10 + 13x + 3x2 = 5 Solving for variable 'x'. Reorder the terms: -10 + -5 + 13x + 3x2 = 5 + -5 Combine like terms: -10 + -5 = -15 -15 + 13x + 3x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -15 + 13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 4.333333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 4.333333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4.333333333x + x2 = 0 + 5 4.333333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 4.333333333x + x2 = 5 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = 5 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 5 + 4.694444446 Combine like terms: 5 + 4.694444446 = 9.694444446 4.694444446 + 4.333333333x + x2 = 9.694444446 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 9.694444446 Calculate the square root of the right side: 3.113590282 Break this problem into two subproblems by setting (x + 2.166666667) equal to 3.113590282 and -3.113590282.Subproblem 1
x + 2.166666667 = 3.113590282 Simplifying x + 2.166666667 = 3.113590282 Reorder the terms: 2.166666667 + x = 3.113590282 Solving 2.166666667 + x = 3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 3.113590282 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 3.113590282 + -2.166666667 x = 3.113590282 + -2.166666667 Combine like terms: 3.113590282 + -2.166666667 = 0.946923615 x = 0.946923615 Simplifying x = 0.946923615Subproblem 2
x + 2.166666667 = -3.113590282 Simplifying x + 2.166666667 = -3.113590282 Reorder the terms: 2.166666667 + x = -3.113590282 Solving 2.166666667 + x = -3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -3.113590282 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -3.113590282 + -2.166666667 x = -3.113590282 + -2.166666667 Combine like terms: -3.113590282 + -2.166666667 = -5.280256949 x = -5.280256949 Simplifying x = -5.280256949Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.946923615, -5.280256949}
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