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Simplifying 1.2 + 0.8x(5x + -3) + -1(2 + -1x) = 0 Reorder the terms: 1.2 + 0.8x(-3 + 5x) + -1(2 + -1x) = 0 1.2 + (-3 * 0.8x + 5x * 0.8x) + -1(2 + -1x) = 0 1.2 + (-2.4x + 4x2) + -1(2 + -1x) = 0 1.2 + -2.4x + 4x2 + (2 * -1 + -1x * -1) = 0 1.2 + -2.4x + 4x2 + (-2 + 1x) = 0 Reorder the terms: 1.2 + -2 + -2.4x + 1x + 4x2 = 0 Combine like terms: 1.2 + -2 = -0.8 -0.8 + -2.4x + 1x + 4x2 = 0 Combine like terms: -2.4x + 1x = -1.4x -0.8 + -1.4x + 4x2 = 0 Solving -0.8 + -1.4x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.2 + -0.35x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.35x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.35x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.35x + x2 = 0 + 0.2 -0.35x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.35x + x2 = 0.2 The x term is -0.35x. Take half its coefficient (-0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. -0.35x + 0.030625 + x2 = 0.2 + 0.030625 Reorder the terms: 0.030625 + -0.35x + x2 = 0.2 + 0.030625 Combine like terms: 0.2 + 0.030625 = 0.230625 0.030625 + -0.35x + x2 = 0.230625 Factor a perfect square on the left side: (x + -0.175)(x + -0.175) = 0.230625 Calculate the square root of the right side: 0.480234318 Break this problem into two subproblems by setting (x + -0.175) equal to 0.480234318 and -0.480234318.Subproblem 1
x + -0.175 = 0.480234318 Simplifying x + -0.175 = 0.480234318 Reorder the terms: -0.175 + x = 0.480234318 Solving -0.175 + x = 0.480234318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.175' to each side of the equation. -0.175 + 0.175 + x = 0.480234318 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + x = 0.480234318 + 0.175 x = 0.480234318 + 0.175 Combine like terms: 0.480234318 + 0.175 = 0.655234318 x = 0.655234318 Simplifying x = 0.655234318Subproblem 2
x + -0.175 = -0.480234318 Simplifying x + -0.175 = -0.480234318 Reorder the terms: -0.175 + x = -0.480234318 Solving -0.175 + x = -0.480234318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.175' to each side of the equation. -0.175 + 0.175 + x = -0.480234318 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + x = -0.480234318 + 0.175 x = -0.480234318 + 0.175 Combine like terms: -0.480234318 + 0.175 = -0.305234318 x = -0.305234318 Simplifying x = -0.305234318Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.655234318, -0.305234318}
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