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Simplifying 4x2 + 37x + 81 = 0 Reorder the terms: 81 + 37x + 4x2 = 0 Solving 81 + 37x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 20.25 + 9.25x + x2 = 0 Move the constant term to the right: Add '-20.25' to each side of the equation. 20.25 + 9.25x + -20.25 + x2 = 0 + -20.25 Reorder the terms: 20.25 + -20.25 + 9.25x + x2 = 0 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + 9.25x + x2 = 0 + -20.25 9.25x + x2 = 0 + -20.25 Combine like terms: 0 + -20.25 = -20.25 9.25x + x2 = -20.25 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 = -20.25 + 21.390625 Reorder the terms: 21.390625 + 9.25x + x2 = -20.25 + 21.390625 Combine like terms: -20.25 + 21.390625 = 1.140625 21.390625 + 9.25x + x2 = 1.140625 Factor a perfect square on the left side: (x + 4.625)(x + 4.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 4.625) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 4.625 = 1.068000468 Simplifying x + 4.625 = 1.068000468 Reorder the terms: 4.625 + x = 1.068000468 Solving 4.625 + x = 1.068000468 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 = 1.068000468 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + x = 1.068000468 + -4.625 x = 1.068000468 + -4.625 Combine like terms: 1.068000468 + -4.625 = -3.556999532 x = -3.556999532 Simplifying x = -3.556999532Subproblem 2
x + 4.625 = -1.068000468 Simplifying x + 4.625 = -1.068000468 Reorder the terms: 4.625 + x = -1.068000468 Solving 4.625 + x = -1.068000468 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 = -1.068000468 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + x = -1.068000468 + -4.625 x = -1.068000468 + -4.625 Combine like terms: -1.068000468 + -4.625 = -5.693000468 x = -5.693000468 Simplifying x = -5.693000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.556999532, -5.693000468}
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