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Simplifying 8x2 + -39x + -125 = 0 Reorder the terms: -125 + -39x + 8x2 = 0 Solving -125 + -39x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15.625 + -4.875x + x2 = 0 Move the constant term to the right: Add '15.625' to each side of the equation. -15.625 + -4.875x + 15.625 + x2 = 0 + 15.625 Reorder the terms: -15.625 + 15.625 + -4.875x + x2 = 0 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + -4.875x + x2 = 0 + 15.625 -4.875x + x2 = 0 + 15.625 Combine like terms: 0 + 15.625 = 15.625 -4.875x + x2 = 15.625 The x term is -4.875x. Take half its coefficient (-2.4375). Square it (5.94140625) and add it to both sides. Add '5.94140625' to each side of the equation. -4.875x + 5.94140625 + x2 = 15.625 + 5.94140625 Reorder the terms: 5.94140625 + -4.875x + x2 = 15.625 + 5.94140625 Combine like terms: 15.625 + 5.94140625 = 21.56640625 5.94140625 + -4.875x + x2 = 21.56640625 Factor a perfect square on the left side: (x + -2.4375)(x + -2.4375) = 21.56640625 Calculate the square root of the right side: 4.643964497 Break this problem into two subproblems by setting (x + -2.4375) equal to 4.643964497 and -4.643964497.Subproblem 1
x + -2.4375 = 4.643964497 Simplifying x + -2.4375 = 4.643964497 Reorder the terms: -2.4375 + x = 4.643964497 Solving -2.4375 + x = 4.643964497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = 4.643964497 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = 4.643964497 + 2.4375 x = 4.643964497 + 2.4375 Combine like terms: 4.643964497 + 2.4375 = 7.081464497 x = 7.081464497 Simplifying x = 7.081464497Subproblem 2
x + -2.4375 = -4.643964497 Simplifying x + -2.4375 = -4.643964497 Reorder the terms: -2.4375 + x = -4.643964497 Solving -2.4375 + x = -4.643964497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = -4.643964497 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = -4.643964497 + 2.4375 x = -4.643964497 + 2.4375 Combine like terms: -4.643964497 + 2.4375 = -2.206464497 x = -2.206464497 Simplifying x = -2.206464497Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.081464497, -2.206464497}
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