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Simplifying 2.5x2 + -5.3x + -8.1 = 0 Reorder the terms: -8.1 + -5.3x + 2.5x2 = 0 Solving -8.1 + -5.3x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -3.24 + -2.12x + x2 = 0 Move the constant term to the right: Add '3.24' to each side of the equation. -3.24 + -2.12x + 3.24 + x2 = 0 + 3.24 Reorder the terms: -3.24 + 3.24 + -2.12x + x2 = 0 + 3.24 Combine like terms: -3.24 + 3.24 = 0.00 0.00 + -2.12x + x2 = 0 + 3.24 -2.12x + x2 = 0 + 3.24 Combine like terms: 0 + 3.24 = 3.24 -2.12x + x2 = 3.24 The x term is -2.12x. Take half its coefficient (-1.06). Square it (1.1236) and add it to both sides. Add '1.1236' to each side of the equation. -2.12x + 1.1236 + x2 = 3.24 + 1.1236 Reorder the terms: 1.1236 + -2.12x + x2 = 3.24 + 1.1236 Combine like terms: 3.24 + 1.1236 = 4.3636 1.1236 + -2.12x + x2 = 4.3636 Factor a perfect square on the left side: (x + -1.06)(x + -1.06) = 4.3636 Calculate the square root of the right side: 2.088923168 Break this problem into two subproblems by setting (x + -1.06) equal to 2.088923168 and -2.088923168.Subproblem 1
x + -1.06 = 2.088923168 Simplifying x + -1.06 = 2.088923168 Reorder the terms: -1.06 + x = 2.088923168 Solving -1.06 + x = 2.088923168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.06' to each side of the equation. -1.06 + 1.06 + x = 2.088923168 + 1.06 Combine like terms: -1.06 + 1.06 = 0.00 0.00 + x = 2.088923168 + 1.06 x = 2.088923168 + 1.06 Combine like terms: 2.088923168 + 1.06 = 3.148923168 x = 3.148923168 Simplifying x = 3.148923168Subproblem 2
x + -1.06 = -2.088923168 Simplifying x + -1.06 = -2.088923168 Reorder the terms: -1.06 + x = -2.088923168 Solving -1.06 + x = -2.088923168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.06' to each side of the equation. -1.06 + 1.06 + x = -2.088923168 + 1.06 Combine like terms: -1.06 + 1.06 = 0.00 0.00 + x = -2.088923168 + 1.06 x = -2.088923168 + 1.06 Combine like terms: -2.088923168 + 1.06 = -1.028923168 x = -1.028923168 Simplifying x = -1.028923168Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.148923168, -1.028923168}
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