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Simplifying (3x + 9.3)(4x + -12.8) = 0 Reorder the terms: (9.3 + 3x)(4x + -12.8) = 0 Reorder the terms: (9.3 + 3x)(-12.8 + 4x) = 0 Multiply (9.3 + 3x) * (-12.8 + 4x) (9.3(-12.8 + 4x) + 3x * (-12.8 + 4x)) = 0 ((-12.8 * 9.3 + 4x * 9.3) + 3x * (-12.8 + 4x)) = 0 ((-119.04 + 37.2x) + 3x * (-12.8 + 4x)) = 0 (-119.04 + 37.2x + (-12.8 * 3x + 4x * 3x)) = 0 (-119.04 + 37.2x + (-38.4x + 12x2)) = 0 Combine like terms: 37.2x + -38.4x = -1.2x (-119.04 + -1.2x + 12x2) = 0 Solving -119.04 + -1.2x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -9.92 + -0.1x + x2 = 0 Move the constant term to the right: Add '9.92' to each side of the equation. -9.92 + -0.1x + 9.92 + x2 = 0 + 9.92 Reorder the terms: -9.92 + 9.92 + -0.1x + x2 = 0 + 9.92 Combine like terms: -9.92 + 9.92 = 0.00 0.00 + -0.1x + x2 = 0 + 9.92 -0.1x + x2 = 0 + 9.92 Combine like terms: 0 + 9.92 = 9.92 -0.1x + x2 = 9.92 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 9.92 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 9.92 + 0.0025 Combine like terms: 9.92 + 0.0025 = 9.9225 0.0025 + -0.1x + x2 = 9.9225 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 9.9225 Calculate the square root of the right side: 3.15 Break this problem into two subproblems by setting (x + -0.05) equal to 3.15 and -3.15.Subproblem 1
x + -0.05 = 3.15 Simplifying x + -0.05 = 3.15 Reorder the terms: -0.05 + x = 3.15 Solving -0.05 + x = 3.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 3.15 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 3.15 + 0.05 x = 3.15 + 0.05 Combine like terms: 3.15 + 0.05 = 3.2 x = 3.2 Simplifying x = 3.2Subproblem 2
x + -0.05 = -3.15 Simplifying x + -0.05 = -3.15 Reorder the terms: -0.05 + x = -3.15 Solving -0.05 + x = -3.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -3.15 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -3.15 + 0.05 x = -3.15 + 0.05 Combine like terms: -3.15 + 0.05 = -3.1 x = -3.1 Simplifying x = -3.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2, -3.1}
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