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Simplifying x2 + 0.75x = 0.5 Reorder the terms: 0.75x + x2 = 0.5 Solving 0.75x + x2 = 0.5 Solving for variable 'x'. Reorder the terms: -0.5 + 0.75x + x2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + 0.75x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.75x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.75x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.75x + x2 = 0.0 + 0.5 0.75x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 0.75x + x2 = 0.5 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.5 + 0.140625 Combine like terms: 0.5 + 0.140625 = 0.640625 0.140625 + 0.75x + x2 = 0.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + 0.375) equal to 0.80039053 and -0.80039053.Subproblem 1
x + 0.375 = 0.80039053 Simplifying x + 0.375 = 0.80039053 Reorder the terms: 0.375 + x = 0.80039053 Solving 0.375 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.80039053 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.80039053 + -0.375 x = 0.80039053 + -0.375 Combine like terms: 0.80039053 + -0.375 = 0.42539053 x = 0.42539053 Simplifying x = 0.42539053Subproblem 2
x + 0.375 = -0.80039053 Simplifying x + 0.375 = -0.80039053 Reorder the terms: 0.375 + x = -0.80039053 Solving 0.375 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.80039053 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.80039053 + -0.375 x = -0.80039053 + -0.375 Combine like terms: -0.80039053 + -0.375 = -1.17539053 x = -1.17539053 Simplifying x = -1.17539053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.42539053, -1.17539053}
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