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Simplifying (x + 0.9)(x + 3.4) = 0 Reorder the terms: (0.9 + x)(x + 3.4) = 0 Reorder the terms: (0.9 + x)(3.4 + x) = 0 Multiply (0.9 + x) * (3.4 + x) (0.9(3.4 + x) + x(3.4 + x)) = 0 ((3.4 * 0.9 + x * 0.9) + x(3.4 + x)) = 0 ((3.06 + 0.9x) + x(3.4 + x)) = 0 (3.06 + 0.9x + (3.4 * x + x * x)) = 0 (3.06 + 0.9x + (3.4x + x2)) = 0 Combine like terms: 0.9x + 3.4x = 4.3x (3.06 + 4.3x + x2) = 0 Solving 3.06 + 4.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3.06' to each side of the equation. 3.06 + 4.3x + -3.06 + x2 = 0 + -3.06 Reorder the terms: 3.06 + -3.06 + 4.3x + x2 = 0 + -3.06 Combine like terms: 3.06 + -3.06 = 0.00 0.00 + 4.3x + x2 = 0 + -3.06 4.3x + x2 = 0 + -3.06 Combine like terms: 0 + -3.06 = -3.06 4.3x + x2 = -3.06 The x term is 4.3x. Take half its coefficient (2.15). Square it (4.6225) and add it to both sides. Add '4.6225' to each side of the equation. 4.3x + 4.6225 + x2 = -3.06 + 4.6225 Reorder the terms: 4.6225 + 4.3x + x2 = -3.06 + 4.6225 Combine like terms: -3.06 + 4.6225 = 1.5625 4.6225 + 4.3x + x2 = 1.5625 Factor a perfect square on the left side: (x + 2.15)(x + 2.15) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x + 2.15) equal to 1.25 and -1.25.Subproblem 1
x + 2.15 = 1.25 Simplifying x + 2.15 = 1.25 Reorder the terms: 2.15 + x = 1.25 Solving 2.15 + x = 1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.15' to each side of the equation. 2.15 + -2.15 + x = 1.25 + -2.15 Combine like terms: 2.15 + -2.15 = 0.00 0.00 + x = 1.25 + -2.15 x = 1.25 + -2.15 Combine like terms: 1.25 + -2.15 = -0.9 x = -0.9 Simplifying x = -0.9Subproblem 2
x + 2.15 = -1.25 Simplifying x + 2.15 = -1.25 Reorder the terms: 2.15 + x = -1.25 Solving 2.15 + x = -1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.15' to each side of the equation. 2.15 + -2.15 + x = -1.25 + -2.15 Combine like terms: 2.15 + -2.15 = 0.00 0.00 + x = -1.25 + -2.15 x = -1.25 + -2.15 Combine like terms: -1.25 + -2.15 = -3.4 x = -3.4 Simplifying x = -3.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.9, -3.4}
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