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Simplifying 8x2 + -39x + 10 = 0 Reorder the terms: 10 + -39x + 8x2 = 0 Solving 10 + -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'. 1.25 + -4.875x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -4.875x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -4.875x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -4.875x + x2 = 0 + -1.25 -4.875x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -4.875x + x2 = -1.25 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 = -1.25 + 5.94140625 Reorder the terms: 5.94140625 + -4.875x + x2 = -1.25 + 5.94140625 Combine like terms: -1.25 + 5.94140625 = 4.69140625 5.94140625 + -4.875x + x2 = 4.69140625 Factor a perfect square on the left side: (x + -2.4375)(x + -2.4375) = 4.69140625 Calculate the square root of the right side: 2.165965431 Break this problem into two subproblems by setting (x + -2.4375) equal to 2.165965431 and -2.165965431.Subproblem 1
x + -2.4375 = 2.165965431 Simplifying x + -2.4375 = 2.165965431 Reorder the terms: -2.4375 + x = 2.165965431 Solving -2.4375 + x = 2.165965431 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 = 2.165965431 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = 2.165965431 + 2.4375 x = 2.165965431 + 2.4375 Combine like terms: 2.165965431 + 2.4375 = 4.603465431 x = 4.603465431 Simplifying x = 4.603465431Subproblem 2
x + -2.4375 = -2.165965431 Simplifying x + -2.4375 = -2.165965431 Reorder the terms: -2.4375 + x = -2.165965431 Solving -2.4375 + x = -2.165965431 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 = -2.165965431 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = -2.165965431 + 2.4375 x = -2.165965431 + 2.4375 Combine like terms: -2.165965431 + 2.4375 = 0.271534569 x = 0.271534569 Simplifying x = 0.271534569Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.603465431, 0.271534569}
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