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Simplifying -0.2x2 + 0.03x + 2 = 0 Reorder the terms: 2 + 0.03x + -0.2x2 = 0 Solving 2 + 0.03x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -10 + -0.15x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.15x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -0.15x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.15x + x2 = 0 + 10 -0.15x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.15x + x2 = 10 The x term is -0.15x. Take half its coefficient (-0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. -0.15x + 0.005625 + x2 = 10 + 0.005625 Reorder the terms: 0.005625 + -0.15x + x2 = 10 + 0.005625 Combine like terms: 10 + 0.005625 = 10.005625 0.005625 + -0.15x + x2 = 10.005625 Factor a perfect square on the left side: (x + -0.075)(x + -0.075) = 10.005625 Calculate the square root of the right side: 3.163166926 Break this problem into two subproblems by setting (x + -0.075) equal to 3.163166926 and -3.163166926.Subproblem 1
x + -0.075 = 3.163166926 Simplifying x + -0.075 = 3.163166926 Reorder the terms: -0.075 + x = 3.163166926 Solving -0.075 + x = 3.163166926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = 3.163166926 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = 3.163166926 + 0.075 x = 3.163166926 + 0.075 Combine like terms: 3.163166926 + 0.075 = 3.238166926 x = 3.238166926 Simplifying x = 3.238166926Subproblem 2
x + -0.075 = -3.163166926 Simplifying x + -0.075 = -3.163166926 Reorder the terms: -0.075 + x = -3.163166926 Solving -0.075 + x = -3.163166926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = -3.163166926 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = -3.163166926 + 0.075 x = -3.163166926 + 0.075 Combine like terms: -3.163166926 + 0.075 = -3.088166926 x = -3.088166926 Simplifying x = -3.088166926Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.238166926, -3.088166926}
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