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Simplifying 3x2 + 3x = 58 Reorder the terms: 3x + 3x2 = 58 Solving 3x + 3x2 = 58 Solving for variable 'x'. Reorder the terms: -58 + 3x + 3x2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -19.33333333 + x + x2 = 0 Move the constant term to the right: Add '19.33333333' to each side of the equation. -19.33333333 + x + 19.33333333 + x2 = 0 + 19.33333333 Reorder the terms: -19.33333333 + 19.33333333 + x + x2 = 0 + 19.33333333 Combine like terms: -19.33333333 + 19.33333333 = 0.00000000 0.00000000 + x + x2 = 0 + 19.33333333 x + x2 = 0 + 19.33333333 Combine like terms: 0 + 19.33333333 = 19.33333333 x + x2 = 19.33333333 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 = 19.33333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 19.33333333 + 0.25 Combine like terms: 19.33333333 + 0.25 = 19.58333333 1.25 + x2 = 19.58333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 19.58333333 Calculate the square root of the right side: 4.425306015 Break this problem into two subproblems by setting (x + 0.5) equal to 4.425306015 and -4.425306015.Subproblem 1
x + 0.5 = 4.425306015 Simplifying x + 0.5 = 4.425306015 Reorder the terms: 0.5 + x = 4.425306015 Solving 0.5 + x = 4.425306015 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 = 4.425306015 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.425306015 + -0.5 x = 4.425306015 + -0.5 Combine like terms: 4.425306015 + -0.5 = 3.925306015 x = 3.925306015 Simplifying x = 3.925306015Subproblem 2
x + 0.5 = -4.425306015 Simplifying x + 0.5 = -4.425306015 Reorder the terms: 0.5 + x = -4.425306015 Solving 0.5 + x = -4.425306015 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 = -4.425306015 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.425306015 + -0.5 x = -4.425306015 + -0.5 Combine like terms: -4.425306015 + -0.5 = -4.925306015 x = -4.925306015 Simplifying x = -4.925306015Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.925306015, -4.925306015}
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