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Simplifying 4x2 + 37x + 40 = 95.5 Reorder the terms: 40 + 37x + 4x2 = 95.5 Solving 40 + 37x + 4x2 = 95.5 Solving for variable 'x'. Reorder the terms: 40 + -95.5 + 37x + 4x2 = 95.5 + -95.5 Combine like terms: 40 + -95.5 = -55.5 -55.5 + 37x + 4x2 = 95.5 + -95.5 Combine like terms: 95.5 + -95.5 = 0.0 -55.5 + 37x + 4x2 = 0.0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.875 + 9.25x + x2 = 0.0 Move the constant term to the right: Add '13.875' to each side of the equation. -13.875 + 9.25x + 13.875 + x2 = 0.0 + 13.875 Reorder the terms: -13.875 + 13.875 + 9.25x + x2 = 0.0 + 13.875 Combine like terms: -13.875 + 13.875 = 0.000 0.000 + 9.25x + x2 = 0.0 + 13.875 9.25x + x2 = 0.0 + 13.875 Combine like terms: 0.0 + 13.875 = 13.875 9.25x + x2 = 13.875 The x term is 9.25x. Take half its coefficient (4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. 9.25x + 21.390625 + x2 = 13.875 + 21.390625 Reorder the terms: 21.390625 + 9.25x + x2 = 13.875 + 21.390625 Combine like terms: 13.875 + 21.390625 = 35.265625 21.390625 + 9.25x + x2 = 35.265625 Factor a perfect square on the left side: (x + 4.625)(x + 4.625) = 35.265625 Calculate the square root of the right side: 5.93848676 Break this problem into two subproblems by setting (x + 4.625) equal to 5.93848676 and -5.93848676.Subproblem 1
x + 4.625 = 5.93848676 Simplifying x + 4.625 = 5.93848676 Reorder the terms: 4.625 + x = 5.93848676 Solving 4.625 + x = 5.93848676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + x = 5.93848676 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + x = 5.93848676 + -4.625 x = 5.93848676 + -4.625 Combine like terms: 5.93848676 + -4.625 = 1.31348676 x = 1.31348676 Simplifying x = 1.31348676Subproblem 2
x + 4.625 = -5.93848676 Simplifying x + 4.625 = -5.93848676 Reorder the terms: 4.625 + x = -5.93848676 Solving 4.625 + x = -5.93848676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + x = -5.93848676 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + x = -5.93848676 + -4.625 x = -5.93848676 + -4.625 Combine like terms: -5.93848676 + -4.625 = -10.56348676 x = -10.56348676 Simplifying x = -10.56348676Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.31348676, -10.56348676}
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