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Simplifying 4x2 + -27x + 37 = 0 Reorder the terms: 37 + -27x + 4x2 = 0 Solving 37 + -27x + 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'. 9.25 + -6.75x + x2 = 0 Move the constant term to the right: Add '-9.25' to each side of the equation. 9.25 + -6.75x + -9.25 + x2 = 0 + -9.25 Reorder the terms: 9.25 + -9.25 + -6.75x + x2 = 0 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + -6.75x + x2 = 0 + -9.25 -6.75x + x2 = 0 + -9.25 Combine like terms: 0 + -9.25 = -9.25 -6.75x + x2 = -9.25 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = -9.25 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = -9.25 + 11.390625 Combine like terms: -9.25 + 11.390625 = 2.140625 11.390625 + -6.75x + x2 = 2.140625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -3.375) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -3.375 = 1.463087489 Simplifying x + -3.375 = 1.463087489 Reorder the terms: -3.375 + x = 1.463087489 Solving -3.375 + x = 1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 1.463087489 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 1.463087489 + 3.375 x = 1.463087489 + 3.375 Combine like terms: 1.463087489 + 3.375 = 4.838087489 x = 4.838087489 Simplifying x = 4.838087489Subproblem 2
x + -3.375 = -1.463087489 Simplifying x + -3.375 = -1.463087489 Reorder the terms: -3.375 + x = -1.463087489 Solving -3.375 + x = -1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -1.463087489 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -1.463087489 + 3.375 x = -1.463087489 + 3.375 Combine like terms: -1.463087489 + 3.375 = 1.911912511 x = 1.911912511 Simplifying x = 1.911912511Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.838087489, 1.911912511}
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