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Simplifying x(5 + -1x) * 0.2 = -1 + -4 + -1 Reorder the terms for easier multiplication: 0.2x(5 + -1x) = -1 + -4 + -1 (5 * 0.2x + -1x * 0.2x) = -1 + -4 + -1 (1x + -0.2x2) = -1 + -4 + -1 Combine like terms: -1 + -4 = -5 1x + -0.2x2 = -5 + -1 Combine like terms: -5 + -1 = -6 1x + -0.2x2 = -6 Solving 1x + -0.2x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 1x + -0.2x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 1x + -0.2x2 = 0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -30 + -5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -5x + x2 = 0 + 30 -5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -5x + x2 = 30 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 30 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 30 + 6.25 Combine like terms: 30 + 6.25 = 36.25 6.25 + -5x + x2 = 36.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -2.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -2.5 = 6.020797289 Simplifying x + -2.5 = 6.020797289 Reorder the terms: -2.5 + x = 6.020797289 Solving -2.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.020797289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.020797289 + 2.5 x = 6.020797289 + 2.5 Combine like terms: 6.020797289 + 2.5 = 8.520797289 x = 8.520797289 Simplifying x = 8.520797289Subproblem 2
x + -2.5 = -6.020797289 Simplifying x + -2.5 = -6.020797289 Reorder the terms: -2.5 + x = -6.020797289 Solving -2.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.020797289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.020797289 + 2.5 x = -6.020797289 + 2.5 Combine like terms: -6.020797289 + 2.5 = -3.520797289 x = -3.520797289 Simplifying x = -3.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.520797289, -3.520797289}
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