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Simplifying 31x2 + 64x + -201 = 0 Reorder the terms: -201 + 64x + 31x2 = 0 Solving -201 + 64x + 31x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. -6.483870968 + 2.064516129x + x2 = 0 Move the constant term to the right: Add '6.483870968' to each side of the equation. -6.483870968 + 2.064516129x + 6.483870968 + x2 = 0 + 6.483870968 Reorder the terms: -6.483870968 + 6.483870968 + 2.064516129x + x2 = 0 + 6.483870968 Combine like terms: -6.483870968 + 6.483870968 = 0.000000000 0.000000000 + 2.064516129x + x2 = 0 + 6.483870968 2.064516129x + x2 = 0 + 6.483870968 Combine like terms: 0 + 6.483870968 = 6.483870968 2.064516129x + x2 = 6.483870968 The x term is 2.064516129x. Take half its coefficient (1.032258065). Square it (1.065556713) and add it to both sides. Add '1.065556713' to each side of the equation. 2.064516129x + 1.065556713 + x2 = 6.483870968 + 1.065556713 Reorder the terms: 1.065556713 + 2.064516129x + x2 = 6.483870968 + 1.065556713 Combine like terms: 6.483870968 + 1.065556713 = 7.549427681 1.065556713 + 2.064516129x + x2 = 7.549427681 Factor a perfect square on the left side: (x + 1.032258065)(x + 1.032258065) = 7.549427681 Calculate the square root of the right side: 2.747622187 Break this problem into two subproblems by setting (x + 1.032258065) equal to 2.747622187 and -2.747622187.Subproblem 1
x + 1.032258065 = 2.747622187 Simplifying x + 1.032258065 = 2.747622187 Reorder the terms: 1.032258065 + x = 2.747622187 Solving 1.032258065 + x = 2.747622187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.032258065' to each side of the equation. 1.032258065 + -1.032258065 + x = 2.747622187 + -1.032258065 Combine like terms: 1.032258065 + -1.032258065 = 0.000000000 0.000000000 + x = 2.747622187 + -1.032258065 x = 2.747622187 + -1.032258065 Combine like terms: 2.747622187 + -1.032258065 = 1.715364122 x = 1.715364122 Simplifying x = 1.715364122Subproblem 2
x + 1.032258065 = -2.747622187 Simplifying x + 1.032258065 = -2.747622187 Reorder the terms: 1.032258065 + x = -2.747622187 Solving 1.032258065 + x = -2.747622187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.032258065' to each side of the equation. 1.032258065 + -1.032258065 + x = -2.747622187 + -1.032258065 Combine like terms: 1.032258065 + -1.032258065 = 0.000000000 0.000000000 + x = -2.747622187 + -1.032258065 x = -2.747622187 + -1.032258065 Combine like terms: -2.747622187 + -1.032258065 = -3.779880252 x = -3.779880252 Simplifying x = -3.779880252Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.715364122, -3.779880252}
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