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Simplifying (x + -0.95)(x + -0.95) = 0 Reorder the terms: (-0.95 + x)(x + -0.95) = 0 Reorder the terms: (-0.95 + x)(-0.95 + x) = 0 Multiply (-0.95 + x) * (-0.95 + x) (-0.95(-0.95 + x) + x(-0.95 + x)) = 0 ((-0.95 * -0.95 + x * -0.95) + x(-0.95 + x)) = 0 ((0.9025 + -0.95x) + x(-0.95 + x)) = 0 (0.9025 + -0.95x + (-0.95 * x + x * x)) = 0 (0.9025 + -0.95x + (-0.95x + x2)) = 0 Combine like terms: -0.95x + -0.95x = -1.9x (0.9025 + -1.9x + x2) = 0 Solving 0.9025 + -1.9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.9025' to each side of the equation. 0.9025 + -1.9x + -0.9025 + x2 = 0 + -0.9025 Reorder the terms: 0.9025 + -0.9025 + -1.9x + x2 = 0 + -0.9025 Combine like terms: 0.9025 + -0.9025 = 0.0000 0.0000 + -1.9x + x2 = 0 + -0.9025 -1.9x + x2 = 0 + -0.9025 Combine like terms: 0 + -0.9025 = -0.9025 -1.9x + x2 = -0.9025 The x term is -1.9x. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9x + 0.9025 + x2 = -0.9025 + 0.9025 Reorder the terms: 0.9025 + -1.9x + x2 = -0.9025 + 0.9025 Combine like terms: -0.9025 + 0.9025 = 0.0000 0.9025 + -1.9x + x2 = 0.0000 Factor a perfect square on the left side: (x + -0.95)(x + -0.95) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -0.95) equal to 0.0000 and 0.0000.Subproblem 1
x + -0.95 = 0.0000 Simplifying x + -0.95 = 0.0000 Reorder the terms: -0.95 + x = 0.0000 Solving -0.95 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 0.0000 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 0.0000 + 0.95 x = 0.0000 + 0.95 Combine like terms: 0.0000 + 0.95 = 0.95 x = 0.95 Simplifying x = 0.95Subproblem 2
x + -0.95 = 0.0000 Simplifying x + -0.95 = 0.0000 Reorder the terms: -0.95 + x = 0.0000 Solving -0.95 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 0.0000 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 0.0000 + 0.95 x = 0.0000 + 0.95 Combine like terms: 0.0000 + 0.95 = 0.95 x = 0.95 Simplifying x = 0.95Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.95, 0.95}
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