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Simplifying (x + -0.5)(x + 0.8) = 0 Reorder the terms: (-0.5 + x)(x + 0.8) = 0 Reorder the terms: (-0.5 + x)(0.8 + x) = 0 Multiply (-0.5 + x) * (0.8 + x) (-0.5(0.8 + x) + x(0.8 + x)) = 0 ((0.8 * -0.5 + x * -0.5) + x(0.8 + x)) = 0 ((-0.4 + -0.5x) + x(0.8 + x)) = 0 (-0.4 + -0.5x + (0.8 * x + x * x)) = 0 (-0.4 + -0.5x + (0.8x + x2)) = 0 Combine like terms: -0.5x + 0.8x = 0.3x (-0.4 + 0.3x + x2) = 0 Solving -0.4 + 0.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.3x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.3x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.3x + x2 = 0 + 0.4 0.3x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.3x + x2 = 0.4 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.4 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.4 + 0.0225 Combine like terms: 0.4 + 0.0225 = 0.4225 0.0225 + 0.3x + x2 = 0.4225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.4225 Calculate the square root of the right side: 0.65 Break this problem into two subproblems by setting (x + 0.15) equal to 0.65 and -0.65.Subproblem 1
x + 0.15 = 0.65 Simplifying x + 0.15 = 0.65 Reorder the terms: 0.15 + x = 0.65 Solving 0.15 + x = 0.65 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.65 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.65 + -0.15 x = 0.65 + -0.15 Combine like terms: 0.65 + -0.15 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 0.15 = -0.65 Simplifying x + 0.15 = -0.65 Reorder the terms: 0.15 + x = -0.65 Solving 0.15 + x = -0.65 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.65 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.65 + -0.15 x = -0.65 + -0.15 Combine like terms: -0.65 + -0.15 = -0.8 x = -0.8 Simplifying x = -0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -0.8}
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