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Simplifying 3x(7x + 8 + -6x + -3) + -4 = 60 Reorder the terms: 3x(8 + -3 + 7x + -6x) + -4 = 60 Combine like terms: 8 + -3 = 5 3x(5 + 7x + -6x) + -4 = 60 Combine like terms: 7x + -6x = 1x 3x(5 + 1x) + -4 = 60 (5 * 3x + 1x * 3x) + -4 = 60 (15x + 3x2) + -4 = 60 Reorder the terms: -4 + 15x + 3x2 = 60 Solving -4 + 15x + 3x2 = 60 Solving for variable 'x'. Reorder the terms: -4 + -60 + 15x + 3x2 = 60 + -60 Combine like terms: -4 + -60 = -64 -64 + 15x + 3x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -64 + 15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21.33333333 + 5x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + 5x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + 5x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + 5x + x2 = 0 + 21.33333333 5x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 5x + x2 = 21.33333333 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 21.33333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 21.33333333 + 6.25 Combine like terms: 21.33333333 + 6.25 = 27.58333333 6.25 + 5x + x2 = 27.58333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 27.58333333 Calculate the square root of the right side: 5.251983752 Break this problem into two subproblems by setting (x + 2.5) equal to 5.251983752 and -5.251983752.Subproblem 1
x + 2.5 = 5.251983752 Simplifying x + 2.5 = 5.251983752 Reorder the terms: 2.5 + x = 5.251983752 Solving 2.5 + x = 5.251983752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.251983752 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.251983752 + -2.5 x = 5.251983752 + -2.5 Combine like terms: 5.251983752 + -2.5 = 2.751983752 x = 2.751983752 Simplifying x = 2.751983752Subproblem 2
x + 2.5 = -5.251983752 Simplifying x + 2.5 = -5.251983752 Reorder the terms: 2.5 + x = -5.251983752 Solving 2.5 + x = -5.251983752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.251983752 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.251983752 + -2.5 x = -5.251983752 + -2.5 Combine like terms: -5.251983752 + -2.5 = -7.751983752 x = -7.751983752 Simplifying x = -7.751983752Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.751983752, -7.751983752}
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