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Simplifying 8x2 + -8x + -49 = 0 Reorder the terms: -49 + -8x + 8x2 = 0 Solving -49 + -8x + 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'. -6.125 + -1x + x2 = 0 Move the constant term to the right: Add '6.125' to each side of the equation. -6.125 + -1x + 6.125 + x2 = 0 + 6.125 Reorder the terms: -6.125 + 6.125 + -1x + x2 = 0 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + -1x + x2 = 0 + 6.125 -1x + x2 = 0 + 6.125 Combine like terms: 0 + 6.125 = 6.125 -1x + x2 = 6.125 The x term is -1x. 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. -1x + 0.25 + x2 = 6.125 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6.125 + 0.25 Combine like terms: 6.125 + 0.25 = 6.375 0.25 + -1x + x2 = 6.375 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 6.375 Calculate the square root of the right side: 2.524876235 Break this problem into two subproblems by setting (x + -0.5) equal to 2.524876235 and -2.524876235.Subproblem 1
x + -0.5 = 2.524876235 Simplifying x + -0.5 = 2.524876235 Reorder the terms: -0.5 + x = 2.524876235 Solving -0.5 + x = 2.524876235 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 = 2.524876235 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.524876235 + 0.5 x = 2.524876235 + 0.5 Combine like terms: 2.524876235 + 0.5 = 3.024876235 x = 3.024876235 Simplifying x = 3.024876235Subproblem 2
x + -0.5 = -2.524876235 Simplifying x + -0.5 = -2.524876235 Reorder the terms: -0.5 + x = -2.524876235 Solving -0.5 + x = -2.524876235 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 = -2.524876235 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.524876235 + 0.5 x = -2.524876235 + 0.5 Combine like terms: -2.524876235 + 0.5 = -2.024876235 x = -2.024876235 Simplifying x = -2.024876235Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.024876235, -2.024876235}
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