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Simplifying x2 + -5.66x + 2.52 = 0 Reorder the terms: 2.52 + -5.66x + x2 = 0 Solving 2.52 + -5.66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2.52' to each side of the equation. 2.52 + -5.66x + -2.52 + x2 = 0 + -2.52 Reorder the terms: 2.52 + -2.52 + -5.66x + x2 = 0 + -2.52 Combine like terms: 2.52 + -2.52 = 0.00 0.00 + -5.66x + x2 = 0 + -2.52 -5.66x + x2 = 0 + -2.52 Combine like terms: 0 + -2.52 = -2.52 -5.66x + x2 = -2.52 The x term is -5.66x. Take half its coefficient (-2.83). Square it (8.0089) and add it to both sides. Add '8.0089' to each side of the equation. -5.66x + 8.0089 + x2 = -2.52 + 8.0089 Reorder the terms: 8.0089 + -5.66x + x2 = -2.52 + 8.0089 Combine like terms: -2.52 + 8.0089 = 5.4889 8.0089 + -5.66x + x2 = 5.4889 Factor a perfect square on the left side: (x + -2.83)(x + -2.83) = 5.4889 Calculate the square root of the right side: 2.342840157 Break this problem into two subproblems by setting (x + -2.83) equal to 2.342840157 and -2.342840157.Subproblem 1
x + -2.83 = 2.342840157 Simplifying x + -2.83 = 2.342840157 Reorder the terms: -2.83 + x = 2.342840157 Solving -2.83 + x = 2.342840157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.83' to each side of the equation. -2.83 + 2.83 + x = 2.342840157 + 2.83 Combine like terms: -2.83 + 2.83 = 0.00 0.00 + x = 2.342840157 + 2.83 x = 2.342840157 + 2.83 Combine like terms: 2.342840157 + 2.83 = 5.172840157 x = 5.172840157 Simplifying x = 5.172840157Subproblem 2
x + -2.83 = -2.342840157 Simplifying x + -2.83 = -2.342840157 Reorder the terms: -2.83 + x = -2.342840157 Solving -2.83 + x = -2.342840157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.83' to each side of the equation. -2.83 + 2.83 + x = -2.342840157 + 2.83 Combine like terms: -2.83 + 2.83 = 0.00 0.00 + x = -2.342840157 + 2.83 x = -2.342840157 + 2.83 Combine like terms: -2.342840157 + 2.83 = 0.487159843 x = 0.487159843 Simplifying x = 0.487159843Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.172840157, 0.487159843}
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