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Simplifying 8x2 + -45x + 62 = 0 Reorder the terms: 62 + -45x + 8x2 = 0 Solving 62 + -45x + 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'. 7.75 + -5.625x + x2 = 0 Move the constant term to the right: Add '-7.75' to each side of the equation. 7.75 + -5.625x + -7.75 + x2 = 0 + -7.75 Reorder the terms: 7.75 + -7.75 + -5.625x + x2 = 0 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + -5.625x + x2 = 0 + -7.75 -5.625x + x2 = 0 + -7.75 Combine like terms: 0 + -7.75 = -7.75 -5.625x + x2 = -7.75 The x term is -5.625x. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625x + 7.91015625 + x2 = -7.75 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = -7.75 + 7.91015625 Combine like terms: -7.75 + 7.91015625 = 0.16015625 7.91015625 + -5.625x + x2 = 0.16015625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 0.16015625 Calculate the square root of the right side: 0.400195265 Break this problem into two subproblems by setting (x + -2.8125) equal to 0.400195265 and -0.400195265.Subproblem 1
x + -2.8125 = 0.400195265 Simplifying x + -2.8125 = 0.400195265 Reorder the terms: -2.8125 + x = 0.400195265 Solving -2.8125 + x = 0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = 0.400195265 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 0.400195265 + 2.8125 x = 0.400195265 + 2.8125 Combine like terms: 0.400195265 + 2.8125 = 3.212695265 x = 3.212695265 Simplifying x = 3.212695265Subproblem 2
x + -2.8125 = -0.400195265 Simplifying x + -2.8125 = -0.400195265 Reorder the terms: -2.8125 + x = -0.400195265 Solving -2.8125 + x = -0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = -0.400195265 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -0.400195265 + 2.8125 x = -0.400195265 + 2.8125 Combine like terms: -0.400195265 + 2.8125 = 2.412304735 x = 2.412304735 Simplifying x = 2.412304735Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.212695265, 2.412304735}
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