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Simplifying 0.6(x + -3)(x + -9) = 0 Reorder the terms: 0.6(-3 + x)(x + -9) = 0 Reorder the terms: 0.6(-3 + x)(-9 + x) = 0 Multiply (-3 + x) * (-9 + x) 0.6(-3(-9 + x) + x(-9 + x)) = 0 0.6((-9 * -3 + x * -3) + x(-9 + x)) = 0 0.6((27 + -3x) + x(-9 + x)) = 0 0.6(27 + -3x + (-9 * x + x * x)) = 0 0.6(27 + -3x + (-9x + x2)) = 0 Combine like terms: -3x + -9x = -12x 0.6(27 + -12x + x2) = 0 (27 * 0.6 + -12x * 0.6 + x2 * 0.6) = 0 (16.2 + -7.2x + 0.6x2) = 0 Solving 16.2 + -7.2x + 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'. 27 + -12x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -12x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -12x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -12x + x2 = 0 + -27 -12x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -12x + x2 = -27 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -27 + 36 Reorder the terms: 36 + -12x + x2 = -27 + 36 Combine like terms: -27 + 36 = 9 36 + -12x + x2 = 9 Factor a perfect square on the left side: (x + -6)(x + -6) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -6) equal to 3 and -3.Subproblem 1
x + -6 = 3 Simplifying x + -6 = 3 Reorder the terms: -6 + x = 3 Solving -6 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3 + 6 x = 3 + 6 Combine like terms: 3 + 6 = 9 x = 9 Simplifying x = 9Subproblem 2
x + -6 = -3 Simplifying x + -6 = -3 Reorder the terms: -6 + x = -3 Solving -6 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3 + 6 x = -3 + 6 Combine like terms: -3 + 6 = 3 x = 3 Simplifying x = 3Solution
The solution to the problem is based on the solutions from the subproblems. x = {9, 3}
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