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Simplifying 2x2 + -5x + 3.125 = 0 Reorder the terms: 3.125 + -5x + 2x2 = 0 Solving 3.125 + -5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5625 + -2.5x + x2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + -2.5x + -1.5625 + x2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + -2.5x + x2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + -2.5x + x2 = 0 + -1.5625 -2.5x + x2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 -2.5x + x2 = -1.5625 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 = -1.5625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.5625 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 1.5625 + -2.5x + x2 = 0.0000 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -1.25) equal to 0.0000 and 0.0000.Subproblem 1
x + -1.25 = 0.0000 Simplifying x + -1.25 = 0.0000 Reorder the terms: -1.25 + x = 0.0000 Solving -1.25 + x = 0.0000 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 = 0.0000 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.0000 + 1.25 x = 0.0000 + 1.25 Combine like terms: 0.0000 + 1.25 = 1.25 x = 1.25 Simplifying x = 1.25Subproblem 2
x + -1.25 = 0.0000 Simplifying x + -1.25 = 0.0000 Reorder the terms: -1.25 + x = 0.0000 Solving -1.25 + x = 0.0000 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 = 0.0000 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.0000 + 1.25 x = 0.0000 + 1.25 Combine like terms: 0.0000 + 1.25 = 1.25 x = 1.25 Simplifying x = 1.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.25, 1.25}
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