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Simplifying 0 = x2 + -2.5x + 1 Reorder the terms: 0 = 1 + -2.5x + x2 Solving 0 = 1 + -2.5x + x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 2.5x + -1x2 = 1 + -2.5x + x2 + -1 + 2.5x + -1x2 Reorder the terms: -1 + 2.5x + -1x2 = 1 + -1 + -2.5x + 2.5x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -1 + 2.5x + -1x2 = 0 + -2.5x + 2.5x + x2 + -1x2 -1 + 2.5x + -1x2 = -2.5x + 2.5x + x2 + -1x2 Combine like terms: -2.5x + 2.5x = 0.0 -1 + 2.5x + -1x2 = 0.0 + x2 + -1x2 -1 + 2.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + 2.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -2.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.5x + x2 = 0 + -1 -2.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.5x + x2 = -1 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -1 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1 + 1.5625 Combine like terms: -1 + 1.5625 = 0.5625 1.5625 + -2.5x + x2 = 0.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + -1.25) equal to 0.75 and -0.75.Subproblem 1
x + -1.25 = 0.75 Simplifying x + -1.25 = 0.75 Reorder the terms: -1.25 + x = 0.75 Solving -1.25 + x = 0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.75 + 1.25 x = 0.75 + 1.25 Combine like terms: 0.75 + 1.25 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.25 = -0.75 Simplifying x + -1.25 = -0.75 Reorder the terms: -1.25 + x = -0.75 Solving -1.25 + x = -0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.75 + 1.25 x = -0.75 + 1.25 Combine like terms: -0.75 + 1.25 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 0.5}
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