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Simplifying -0.05x2 + 2.7x + 5.1 = 0 Reorder the terms: 5.1 + 2.7x + -0.05x2 = 0 Solving 5.1 + 2.7x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -102 + -54x + x2 = 0 Move the constant term to the right: Add '102' to each side of the equation. -102 + -54x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + -54x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + -54x + x2 = 0 + 102 -54x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 -54x + x2 = 102 The x term is -54x. Take half its coefficient (-27). Square it (729) and add it to both sides. Add '729' to each side of the equation. -54x + 729 + x2 = 102 + 729 Reorder the terms: 729 + -54x + x2 = 102 + 729 Combine like terms: 102 + 729 = 831 729 + -54x + x2 = 831 Factor a perfect square on the left side: (x + -27)(x + -27) = 831 Calculate the square root of the right side: 28.827070611 Break this problem into two subproblems by setting (x + -27) equal to 28.827070611 and -28.827070611.Subproblem 1
x + -27 = 28.827070611 Simplifying x + -27 = 28.827070611 Reorder the terms: -27 + x = 28.827070611 Solving -27 + x = 28.827070611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = 28.827070611 + 27 Combine like terms: -27 + 27 = 0 0 + x = 28.827070611 + 27 x = 28.827070611 + 27 Combine like terms: 28.827070611 + 27 = 55.827070611 x = 55.827070611 Simplifying x = 55.827070611Subproblem 2
x + -27 = -28.827070611 Simplifying x + -27 = -28.827070611 Reorder the terms: -27 + x = -28.827070611 Solving -27 + x = -28.827070611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = -28.827070611 + 27 Combine like terms: -27 + 27 = 0 0 + x = -28.827070611 + 27 x = -28.827070611 + 27 Combine like terms: -28.827070611 + 27 = -1.827070611 x = -1.827070611 Simplifying x = -1.827070611Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.827070611, -1.827070611}
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