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Simplifying 0.6(x + -6)(x + 10) = 0 Reorder the terms: 0.6(-6 + x)(x + 10) = 0 Reorder the terms: 0.6(-6 + x)(10 + x) = 0 Multiply (-6 + x) * (10 + x) 0.6(-6(10 + x) + x(10 + x)) = 0 0.6((10 * -6 + x * -6) + x(10 + x)) = 0 0.6((-60 + -6x) + x(10 + x)) = 0 0.6(-60 + -6x + (10 * x + x * x)) = 0 0.6(-60 + -6x + (10x + x2)) = 0 Combine like terms: -6x + 10x = 4x 0.6(-60 + 4x + x2) = 0 (-60 * 0.6 + 4x * 0.6 + x2 * 0.6) = 0 (-36 + 2.4x + 0.6x2) = 0 Solving -36 + 2.4x + 0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -60 + 4x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 4x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 4x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 4x + x2 = 0 + 60 4x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 4x + x2 = 60 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 60 + 4 Reorder the terms: 4 + 4x + x2 = 60 + 4 Combine like terms: 60 + 4 = 64 4 + 4x + x2 = 64 Factor a perfect square on the left side: (x + 2)(x + 2) = 64 Calculate the square root of the right side: 8 Break this problem into two subproblems by setting (x + 2) equal to 8 and -8.Subproblem 1
x + 2 = 8 Simplifying x + 2 = 8 Reorder the terms: 2 + x = 8 Solving 2 + x = 8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8 + -2 x = 8 + -2 Combine like terms: 8 + -2 = 6 x = 6 Simplifying x = 6Subproblem 2
x + 2 = -8 Simplifying x + 2 = -8 Reorder the terms: 2 + x = -8 Solving 2 + x = -8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8 + -2 x = -8 + -2 Combine like terms: -8 + -2 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, -10}
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