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Simplifying 8x2 + -87x + 45 = 0 Reorder the terms: 45 + -87x + 8x2 = 0 Solving 45 + -87x + 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'. 5.625 + -10.875x + x2 = 0 Move the constant term to the right: Add '-5.625' to each side of the equation. 5.625 + -10.875x + -5.625 + x2 = 0 + -5.625 Reorder the terms: 5.625 + -5.625 + -10.875x + x2 = 0 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + -10.875x + x2 = 0 + -5.625 -10.875x + x2 = 0 + -5.625 Combine like terms: 0 + -5.625 = -5.625 -10.875x + x2 = -5.625 The x term is -10.875x. Take half its coefficient (-5.4375). Square it (29.56640625) and add it to both sides. Add '29.56640625' to each side of the equation. -10.875x + 29.56640625 + x2 = -5.625 + 29.56640625 Reorder the terms: 29.56640625 + -10.875x + x2 = -5.625 + 29.56640625 Combine like terms: -5.625 + 29.56640625 = 23.94140625 29.56640625 + -10.875x + x2 = 23.94140625 Factor a perfect square on the left side: (x + -5.4375)(x + -5.4375) = 23.94140625 Calculate the square root of the right side: 4.892995632 Break this problem into two subproblems by setting (x + -5.4375) equal to 4.892995632 and -4.892995632.Subproblem 1
x + -5.4375 = 4.892995632 Simplifying x + -5.4375 = 4.892995632 Reorder the terms: -5.4375 + x = 4.892995632 Solving -5.4375 + x = 4.892995632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.4375' to each side of the equation. -5.4375 + 5.4375 + x = 4.892995632 + 5.4375 Combine like terms: -5.4375 + 5.4375 = 0.0000 0.0000 + x = 4.892995632 + 5.4375 x = 4.892995632 + 5.4375 Combine like terms: 4.892995632 + 5.4375 = 10.330495632 x = 10.330495632 Simplifying x = 10.330495632Subproblem 2
x + -5.4375 = -4.892995632 Simplifying x + -5.4375 = -4.892995632 Reorder the terms: -5.4375 + x = -4.892995632 Solving -5.4375 + x = -4.892995632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.4375' to each side of the equation. -5.4375 + 5.4375 + x = -4.892995632 + 5.4375 Combine like terms: -5.4375 + 5.4375 = 0.0000 0.0000 + x = -4.892995632 + 5.4375 x = -4.892995632 + 5.4375 Combine like terms: -4.892995632 + 5.4375 = 0.544504368 x = 0.544504368 Simplifying x = 0.544504368Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.330495632, 0.544504368}
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