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Simplifying (6x + -9)(4x + 0.4) = 0 Reorder the terms: (-9 + 6x)(4x + 0.4) = 0 Reorder the terms: (-9 + 6x)(0.4 + 4x) = 0 Multiply (-9 + 6x) * (0.4 + 4x) (-9(0.4 + 4x) + 6x * (0.4 + 4x)) = 0 ((0.4 * -9 + 4x * -9) + 6x * (0.4 + 4x)) = 0 ((-3.6 + -36x) + 6x * (0.4 + 4x)) = 0 (-3.6 + -36x + (0.4 * 6x + 4x * 6x)) = 0 (-3.6 + -36x + (2.4x + 24x2)) = 0 Combine like terms: -36x + 2.4x = -33.6x (-3.6 + -33.6x + 24x2) = 0 Solving -3.6 + -33.6x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.15 + -1.4x + x2 = 0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + -1.4x + 0.15 + x2 = 0 + 0.15 Reorder the terms: -0.15 + 0.15 + -1.4x + x2 = 0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + -1.4x + x2 = 0 + 0.15 -1.4x + x2 = 0 + 0.15 Combine like terms: 0 + 0.15 = 0.15 -1.4x + x2 = 0.15 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.15 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.15 + 0.49 Combine like terms: 0.15 + 0.49 = 0.64 0.49 + -1.4x + x2 = 0.64 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.64 Calculate the square root of the right side: 0.8 Break this problem into two subproblems by setting (x + -0.7) equal to 0.8 and -0.8.Subproblem 1
x + -0.7 = 0.8 Simplifying x + -0.7 = 0.8 Reorder the terms: -0.7 + x = 0.8 Solving -0.7 + x = 0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.8 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.8 + 0.7 x = 0.8 + 0.7 Combine like terms: 0.8 + 0.7 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + -0.7 = -0.8 Simplifying x + -0.7 = -0.8 Reorder the terms: -0.7 + x = -0.8 Solving -0.7 + x = -0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.8 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.8 + 0.7 x = -0.8 + 0.7 Combine like terms: -0.8 + 0.7 = -0.1 x = -0.1 Simplifying x = -0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -0.1}
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