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Simplifying 4x2 + -27x + 5 = 0 Reorder the terms: 5 + -27x + 4x2 = 0 Solving 5 + -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'. 1.25 + -6.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -6.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -6.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -6.75x + x2 = 0 + -1.25 -6.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -6.75x + x2 = -1.25 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 = -1.25 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = -1.25 + 11.390625 Combine like terms: -1.25 + 11.390625 = 10.140625 11.390625 + -6.75x + x2 = 10.140625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 10.140625 Calculate the square root of the right side: 3.184434801 Break this problem into two subproblems by setting (x + -3.375) equal to 3.184434801 and -3.184434801.Subproblem 1
x + -3.375 = 3.184434801 Simplifying x + -3.375 = 3.184434801 Reorder the terms: -3.375 + x = 3.184434801 Solving -3.375 + x = 3.184434801 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 = 3.184434801 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 3.184434801 + 3.375 x = 3.184434801 + 3.375 Combine like terms: 3.184434801 + 3.375 = 6.559434801 x = 6.559434801 Simplifying x = 6.559434801Subproblem 2
x + -3.375 = -3.184434801 Simplifying x + -3.375 = -3.184434801 Reorder the terms: -3.375 + x = -3.184434801 Solving -3.375 + x = -3.184434801 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 = -3.184434801 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -3.184434801 + 3.375 x = -3.184434801 + 3.375 Combine like terms: -3.184434801 + 3.375 = 0.190565199 x = 0.190565199 Simplifying x = 0.190565199Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.559434801, 0.190565199}
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