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Simplifying 0.4(x + -1)(x + -5) = 0 Reorder the terms: 0.4(-1 + x)(x + -5) = 0 Reorder the terms: 0.4(-1 + x)(-5 + x) = 0 Multiply (-1 + x) * (-5 + x) 0.4(-1(-5 + x) + x(-5 + x)) = 0 0.4((-5 * -1 + x * -1) + x(-5 + x)) = 0 0.4((5 + -1x) + x(-5 + x)) = 0 0.4(5 + -1x + (-5 * x + x * x)) = 0 0.4(5 + -1x + (-5x + x2)) = 0 Combine like terms: -1x + -5x = -6x 0.4(5 + -6x + x2) = 0 (5 * 0.4 + -6x * 0.4 + x2 * 0.4) = 0 (2 + -2.4x + 0.4x2) = 0 Solving 2 + -2.4x + 0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 5 + -6x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -6x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -6x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x + x2 = 0 + -5 -6x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6x + x2 = -5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -5 + 9 Reorder the terms: 9 + -6x + x2 = -5 + 9 Combine like terms: -5 + 9 = 4 9 + -6x + x2 = 4 Factor a perfect square on the left side: (x + -3)(x + -3) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -3) equal to 2 and -2.Subproblem 1
x + -3 = 2 Simplifying x + -3 = 2 Reorder the terms: -3 + x = 2 Solving -3 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2 + 3 x = 2 + 3 Combine like terms: 2 + 3 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -3 = -2 Simplifying x + -3 = -2 Reorder the terms: -3 + x = -2 Solving -3 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2 + 3 x = -2 + 3 Combine like terms: -2 + 3 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 1}
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