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Simplifying 8x2 + -1x + -70 = 0 Reorder the terms: -70 + -1x + 8x2 = 0 Solving -70 + -1x + 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'. -8.75 + -0.125x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -0.125x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -0.125x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -0.125x + x2 = 0 + 8.75 -0.125x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -0.125x + x2 = 8.75 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 8.75 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 8.75 + 0.00390625 Combine like terms: 8.75 + 0.00390625 = 8.75390625 0.00390625 + -0.125x + x2 = 8.75390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 8.75390625 Calculate the square root of the right side: 2.958700095 Break this problem into two subproblems by setting (x + -0.0625) equal to 2.958700095 and -2.958700095.Subproblem 1
x + -0.0625 = 2.958700095 Simplifying x + -0.0625 = 2.958700095 Reorder the terms: -0.0625 + x = 2.958700095 Solving -0.0625 + x = 2.958700095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 2.958700095 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 2.958700095 + 0.0625 x = 2.958700095 + 0.0625 Combine like terms: 2.958700095 + 0.0625 = 3.021200095 x = 3.021200095 Simplifying x = 3.021200095Subproblem 2
x + -0.0625 = -2.958700095 Simplifying x + -0.0625 = -2.958700095 Reorder the terms: -0.0625 + x = -2.958700095 Solving -0.0625 + x = -2.958700095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -2.958700095 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -2.958700095 + 0.0625 x = -2.958700095 + 0.0625 Combine like terms: -2.958700095 + 0.0625 = -2.896200095 x = -2.896200095 Simplifying x = -2.896200095Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.021200095, -2.896200095}
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