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Simplifying x2 + 0.2x + -0.24 = 0 Reorder the terms: -0.24 + 0.2x + x2 = 0 Solving -0.24 + 0.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + 0.2x + 0.24 + x2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + 0.2x + x2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + 0.2x + x2 = 0 + 0.24 0.2x + x2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 0.2x + x2 = 0.24 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.24 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.24 + 0.01 Combine like terms: 0.24 + 0.01 = 0.25 0.01 + 0.2x + x2 = 0.25 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + 0.1) equal to 0.5 and -0.5.Subproblem 1
x + 0.1 = 0.5 Simplifying x + 0.1 = 0.5 Reorder the terms: 0.1 + x = 0.5 Solving 0.1 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.5 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.5 + -0.1 x = 0.5 + -0.1 Combine like terms: 0.5 + -0.1 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + 0.1 = -0.5 Simplifying x + 0.1 = -0.5 Reorder the terms: 0.1 + x = -0.5 Solving 0.1 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.5 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.5 + -0.1 x = -0.5 + -0.1 Combine like terms: -0.5 + -0.1 = -0.6 x = -0.6 Simplifying x = -0.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, -0.6}
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