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Simplifying (x + 9)(3x + -3.6) = 0 Reorder the terms: (9 + x)(3x + -3.6) = 0 Reorder the terms: (9 + x)(-3.6 + 3x) = 0 Multiply (9 + x) * (-3.6 + 3x) (9(-3.6 + 3x) + x(-3.6 + 3x)) = 0 ((-3.6 * 9 + 3x * 9) + x(-3.6 + 3x)) = 0 ((-32.4 + 27x) + x(-3.6 + 3x)) = 0 (-32.4 + 27x + (-3.6 * x + 3x * x)) = 0 (-32.4 + 27x + (-3.6x + 3x2)) = 0 Combine like terms: 27x + -3.6x = 23.4x (-32.4 + 23.4x + 3x2) = 0 Solving -32.4 + 23.4x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.8 + 7.8x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + 7.8x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + 7.8x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + 7.8x + x2 = 0 + 10.8 7.8x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 7.8x + x2 = 10.8 The x term is 7.8x. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8x + 15.21 + x2 = 10.8 + 15.21 Reorder the terms: 15.21 + 7.8x + x2 = 10.8 + 15.21 Combine like terms: 10.8 + 15.21 = 26.01 15.21 + 7.8x + x2 = 26.01 Factor a perfect square on the left side: (x + 3.9)(x + 3.9) = 26.01 Calculate the square root of the right side: 5.1 Break this problem into two subproblems by setting (x + 3.9) equal to 5.1 and -5.1.Subproblem 1
x + 3.9 = 5.1 Simplifying x + 3.9 = 5.1 Reorder the terms: 3.9 + x = 5.1 Solving 3.9 + x = 5.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = 5.1 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = 5.1 + -3.9 x = 5.1 + -3.9 Combine like terms: 5.1 + -3.9 = 1.2 x = 1.2 Simplifying x = 1.2Subproblem 2
x + 3.9 = -5.1 Simplifying x + 3.9 = -5.1 Reorder the terms: 3.9 + x = -5.1 Solving 3.9 + x = -5.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = -5.1 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = -5.1 + -3.9 x = -5.1 + -3.9 Combine like terms: -5.1 + -3.9 = -9 x = -9 Simplifying x = -9Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2, -9}
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