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Simplifying (x + -0.4)(x + 0.9) = 0 Reorder the terms: (-0.4 + x)(x + 0.9) = 0 Reorder the terms: (-0.4 + x)(0.9 + x) = 0 Multiply (-0.4 + x) * (0.9 + x) (-0.4(0.9 + x) + x(0.9 + x)) = 0 ((0.9 * -0.4 + x * -0.4) + x(0.9 + x)) = 0 ((-0.36 + -0.4x) + x(0.9 + x)) = 0 (-0.36 + -0.4x + (0.9 * x + x * x)) = 0 (-0.36 + -0.4x + (0.9x + x2)) = 0 Combine like terms: -0.4x + 0.9x = 0.5x (-0.36 + 0.5x + x2) = 0 Solving -0.36 + 0.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + 0.5x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + 0.5x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + 0.5x + x2 = 0 + 0.36 0.5x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 0.5x + x2 = 0.36 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.36 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.36 + 0.0625 Combine like terms: 0.36 + 0.0625 = 0.4225 0.0625 + 0.5x + x2 = 0.4225 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.4225 Calculate the square root of the right side: 0.65 Break this problem into two subproblems by setting (x + 0.25) equal to 0.65 and -0.65.Subproblem 1
x + 0.25 = 0.65 Simplifying x + 0.25 = 0.65 Reorder the terms: 0.25 + x = 0.65 Solving 0.25 + x = 0.65 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.65 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.65 + -0.25 x = 0.65 + -0.25 Combine like terms: 0.65 + -0.25 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + 0.25 = -0.65 Simplifying x + 0.25 = -0.65 Reorder the terms: 0.25 + x = -0.65 Solving 0.25 + x = -0.65 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.65 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.65 + -0.25 x = -0.65 + -0.25 Combine like terms: -0.65 + -0.25 = -0.9 x = -0.9 Simplifying x = -0.9Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, -0.9}
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