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Simplifying (-0.125x2 + 2x) + -1(0.1875x2 + -3) = 2.5 Reorder the terms: (2x + -0.125x2) + -1(0.1875x2 + -3) = 2.5 Remove parenthesis around (2x + -0.125x2) 2x + -0.125x2 + -1(0.1875x2 + -3) = 2.5 Reorder the terms: 2x + -0.125x2 + -1(-3 + 0.1875x2) = 2.5 2x + -0.125x2 + (-3 * -1 + 0.1875x2 * -1) = 2.5 2x + -0.125x2 + (3 + -0.1875x2) = 2.5 Reorder the terms: 3 + 2x + -0.125x2 + -0.1875x2 = 2.5 Combine like terms: -0.125x2 + -0.1875x2 = -0.3125x2 3 + 2x + -0.3125x2 = 2.5 Solving 3 + 2x + -0.3125x2 = 2.5 Solving for variable 'x'. Reorder the terms: 3 + -2.5 + 2x + -0.3125x2 = 2.5 + -2.5 Combine like terms: 3 + -2.5 = 0.5 0.5 + 2x + -0.3125x2 = 2.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.5 + 2x + -0.3125x2 = 0.0 Begin completing the square. Divide all terms by -0.3125 the coefficient of the squared term: Divide each side by '-0.3125'. -1.6 + -6.4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -6.4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -6.4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -6.4x + x2 = 0 + 1.6 -6.4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -6.4x + x2 = 1.6 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = 1.6 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = 1.6 + 10.24 Combine like terms: 1.6 + 10.24 = 11.84 10.24 + -6.4x + x2 = 11.84 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 11.84 Calculate the square root of the right side: 3.440930107 Break this problem into two subproblems by setting (x + -3.2) equal to 3.440930107 and -3.440930107.Subproblem 1
x + -3.2 = 3.440930107 Simplifying x + -3.2 = 3.440930107 Reorder the terms: -3.2 + x = 3.440930107 Solving -3.2 + x = 3.440930107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 3.440930107 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 3.440930107 + 3.2 x = 3.440930107 + 3.2 Combine like terms: 3.440930107 + 3.2 = 6.640930107 x = 6.640930107 Simplifying x = 6.640930107Subproblem 2
x + -3.2 = -3.440930107 Simplifying x + -3.2 = -3.440930107 Reorder the terms: -3.2 + x = -3.440930107 Solving -3.2 + x = -3.440930107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -3.440930107 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -3.440930107 + 3.2 x = -3.440930107 + 3.2 Combine like terms: -3.440930107 + 3.2 = -0.240930107 x = -0.240930107 Simplifying x = -0.240930107Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.640930107, -0.240930107}
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