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Simplifying 61 + -1(3x + 15) = 3(x + 6) * x Reorder the terms: 61 + -1(15 + 3x) = 3(x + 6) * x 61 + (15 * -1 + 3x * -1) = 3(x + 6) * x 61 + (-15 + -3x) = 3(x + 6) * x Combine like terms: 61 + -15 = 46 46 + -3x = 3(x + 6) * x Reorder the terms: 46 + -3x = 3(6 + x) * x Reorder the terms for easier multiplication: 46 + -3x = 3x(6 + x) 46 + -3x = (6 * 3x + x * 3x) 46 + -3x = (18x + 3x2) Solving 46 + -3x = 18x + 3x2 Solving for variable 'x'. Combine like terms: -3x + -18x = -21x 46 + -21x + -3x2 = 18x + 3x2 + -18x + -3x2 Reorder the terms: 46 + -21x + -3x2 = 18x + -18x + 3x2 + -3x2 Combine like terms: 18x + -18x = 0 46 + -21x + -3x2 = 0 + 3x2 + -3x2 46 + -21x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 46 + -21x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -15.33333333 + 7x + x2 = 0 Move the constant term to the right: Add '15.33333333' to each side of the equation. -15.33333333 + 7x + 15.33333333 + x2 = 0 + 15.33333333 Reorder the terms: -15.33333333 + 15.33333333 + 7x + x2 = 0 + 15.33333333 Combine like terms: -15.33333333 + 15.33333333 = 0.00000000 0.00000000 + 7x + x2 = 0 + 15.33333333 7x + x2 = 0 + 15.33333333 Combine like terms: 0 + 15.33333333 = 15.33333333 7x + x2 = 15.33333333 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 15.33333333 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 15.33333333 + 12.25 Combine like terms: 15.33333333 + 12.25 = 27.58333333 12.25 + 7x + x2 = 27.58333333 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 27.58333333 Calculate the square root of the right side: 5.251983752 Break this problem into two subproblems by setting (x + 3.5) equal to 5.251983752 and -5.251983752.Subproblem 1
x + 3.5 = 5.251983752 Simplifying x + 3.5 = 5.251983752 Reorder the terms: 3.5 + x = 5.251983752 Solving 3.5 + x = 5.251983752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.251983752 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.251983752 + -3.5 x = 5.251983752 + -3.5 Combine like terms: 5.251983752 + -3.5 = 1.751983752 x = 1.751983752 Simplifying x = 1.751983752Subproblem 2
x + 3.5 = -5.251983752 Simplifying x + 3.5 = -5.251983752 Reorder the terms: 3.5 + x = -5.251983752 Solving 3.5 + x = -5.251983752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.251983752 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.251983752 + -3.5 x = -5.251983752 + -3.5 Combine like terms: -5.251983752 + -3.5 = -8.751983752 x = -8.751983752 Simplifying x = -8.751983752Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.751983752, -8.751983752}
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