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Simplifying x2 + -1x + 0.2496 = 0 Reorder the terms: 0.2496 + -1x + x2 = 0 Solving 0.2496 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.2496' to each side of the equation. 0.2496 + -1x + -0.2496 + x2 = 0 + -0.2496 Reorder the terms: 0.2496 + -0.2496 + -1x + x2 = 0 + -0.2496 Combine like terms: 0.2496 + -0.2496 = 0.0000 0.0000 + -1x + x2 = 0 + -0.2496 -1x + x2 = 0 + -0.2496 Combine like terms: 0 + -0.2496 = -0.2496 -1x + x2 = -0.2496 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.2496 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.2496 + 0.25 Combine like terms: -0.2496 + 0.25 = 0.0004 0.25 + -1x + x2 = 0.0004 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0004 Calculate the square root of the right side: 0.02 Break this problem into two subproblems by setting (x + -0.5) equal to 0.02 and -0.02.Subproblem 1
x + -0.5 = 0.02 Simplifying x + -0.5 = 0.02 Reorder the terms: -0.5 + x = 0.02 Solving -0.5 + x = 0.02 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.02 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.02 + 0.5 x = 0.02 + 0.5 Combine like terms: 0.02 + 0.5 = 0.52 x = 0.52 Simplifying x = 0.52Subproblem 2
x + -0.5 = -0.02 Simplifying x + -0.5 = -0.02 Reorder the terms: -0.5 + x = -0.02 Solving -0.5 + x = -0.02 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.02 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.02 + 0.5 x = -0.02 + 0.5 Combine like terms: -0.02 + 0.5 = 0.48 x = 0.48 Simplifying x = 0.48Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.52, 0.48}
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