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Simplifying 3x2 + 3x = 82 Reorder the terms: 3x + 3x2 = 82 Solving 3x + 3x2 = 82 Solving for variable 'x'. Reorder the terms: -82 + 3x + 3x2 = 82 + -82 Combine like terms: 82 + -82 = 0 -82 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -27.33333333 + x + x2 = 0 Move the constant term to the right: Add '27.33333333' to each side of the equation. -27.33333333 + x + 27.33333333 + x2 = 0 + 27.33333333 Reorder the terms: -27.33333333 + 27.33333333 + x + x2 = 0 + 27.33333333 Combine like terms: -27.33333333 + 27.33333333 = 0.00000000 0.00000000 + x + x2 = 0 + 27.33333333 x + x2 = 0 + 27.33333333 Combine like terms: 0 + 27.33333333 = 27.33333333 x + x2 = 27.33333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 27.33333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 27.33333333 + 0.25 Combine like terms: 27.33333333 + 0.25 = 27.58333333 1.25 + x2 = 27.58333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 27.58333333 Calculate the square root of the right side: 5.251983752 Break this problem into two subproblems by setting (x + 0.5) equal to 5.251983752 and -5.251983752.Subproblem 1
x + 0.5 = 5.251983752 Simplifying x + 0.5 = 5.251983752 Reorder the terms: 0.5 + x = 5.251983752 Solving 0.5 + x = 5.251983752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.251983752 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.251983752 + -0.5 x = 5.251983752 + -0.5 Combine like terms: 5.251983752 + -0.5 = 4.751983752 x = 4.751983752 Simplifying x = 4.751983752Subproblem 2
x + 0.5 = -5.251983752 Simplifying x + 0.5 = -5.251983752 Reorder the terms: 0.5 + x = -5.251983752 Solving 0.5 + x = -5.251983752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.251983752 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.251983752 + -0.5 x = -5.251983752 + -0.5 Combine like terms: -5.251983752 + -0.5 = -5.751983752 x = -5.751983752 Simplifying x = -5.751983752Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.751983752, -5.751983752}
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