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Simplifying 8x2 + 45x + -450 = 0 Reorder the terms: -450 + 45x + 8x2 = 0 Solving -450 + 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'. -56.25 + 5.625x + x2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + 5.625x + 56.25 + x2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + 5.625x + x2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + 5.625x + x2 = 0 + 56.25 5.625x + x2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 5.625x + x2 = 56.25 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 = 56.25 + 7.91015625 Reorder the terms: 7.91015625 + 5.625x + x2 = 56.25 + 7.91015625 Combine like terms: 56.25 + 7.91015625 = 64.16015625 7.91015625 + 5.625x + x2 = 64.16015625 Factor a perfect square on the left side: (x + 2.8125)(x + 2.8125) = 64.16015625 Calculate the square root of the right side: 8.010003511 Break this problem into two subproblems by setting (x + 2.8125) equal to 8.010003511 and -8.010003511.Subproblem 1
x + 2.8125 = 8.010003511 Simplifying x + 2.8125 = 8.010003511 Reorder the terms: 2.8125 + x = 8.010003511 Solving 2.8125 + x = 8.010003511 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 = 8.010003511 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + x = 8.010003511 + -2.8125 x = 8.010003511 + -2.8125 Combine like terms: 8.010003511 + -2.8125 = 5.197503511 x = 5.197503511 Simplifying x = 5.197503511Subproblem 2
x + 2.8125 = -8.010003511 Simplifying x + 2.8125 = -8.010003511 Reorder the terms: 2.8125 + x = -8.010003511 Solving 2.8125 + x = -8.010003511 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 = -8.010003511 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + x = -8.010003511 + -2.8125 x = -8.010003511 + -2.8125 Combine like terms: -8.010003511 + -2.8125 = -10.822503511 x = -10.822503511 Simplifying x = -10.822503511Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.197503511, -10.822503511}
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