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Simplifying x2 + -1.2x + 0.25 = 0 Reorder the terms: 0.25 + -1.2x + x2 = 0 Solving 0.25 + -1.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.2x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.2x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.2x + x2 = 0 + -0.25 -1.2x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.2x + x2 = -0.25 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.25 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.25 + 0.36 Combine like terms: -0.25 + 0.36 = 0.11 0.36 + -1.2x + x2 = 0.11 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.11 Calculate the square root of the right side: 0.331662479 Break this problem into two subproblems by setting (x + -0.6) equal to 0.331662479 and -0.331662479.Subproblem 1
x + -0.6 = 0.331662479 Simplifying x + -0.6 = 0.331662479 Reorder the terms: -0.6 + x = 0.331662479 Solving -0.6 + x = 0.331662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.331662479 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.331662479 + 0.6 x = 0.331662479 + 0.6 Combine like terms: 0.331662479 + 0.6 = 0.931662479 x = 0.931662479 Simplifying x = 0.931662479Subproblem 2
x + -0.6 = -0.331662479 Simplifying x + -0.6 = -0.331662479 Reorder the terms: -0.6 + x = -0.331662479 Solving -0.6 + x = -0.331662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.331662479 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.331662479 + 0.6 x = -0.331662479 + 0.6 Combine like terms: -0.331662479 + 0.6 = 0.268337521 x = 0.268337521 Simplifying x = 0.268337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.931662479, 0.268337521}
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