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Simplifying (0.2x + -1)(0.4 + -0.2x) = 0 Reorder the terms: (-1 + 0.2x)(0.4 + -0.2x) = 0 Multiply (-1 + 0.2x) * (0.4 + -0.2x) (-1(0.4 + -0.2x) + 0.2x * (0.4 + -0.2x)) = 0 ((0.4 * -1 + -0.2x * -1) + 0.2x * (0.4 + -0.2x)) = 0 ((-0.4 + 0.2x) + 0.2x * (0.4 + -0.2x)) = 0 (-0.4 + 0.2x + (0.4 * 0.2x + -0.2x * 0.2x)) = 0 (-0.4 + 0.2x + (0.08x + -0.04x2)) = 0 Combine like terms: 0.2x + 0.08x = 0.28x (-0.4 + 0.28x + -0.04x2) = 0 Solving -0.4 + 0.28x + -0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. 10 + -7x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -7x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -7x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7x + x2 = 0 + -10 -7x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -7x + x2 = -10 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -10 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -10 + 12.25 Combine like terms: -10 + 12.25 = 2.25 12.25 + -7x + x2 = 2.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + -3.5) equal to 1.5 and -1.5.Subproblem 1
x + -3.5 = 1.5 Simplifying x + -3.5 = 1.5 Reorder the terms: -3.5 + x = 1.5 Solving -3.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.5 + 3.5 x = 1.5 + 3.5 Combine like terms: 1.5 + 3.5 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -3.5 = -1.5 Simplifying x + -3.5 = -1.5 Reorder the terms: -3.5 + x = -1.5 Solving -3.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.5 + 3.5 x = -1.5 + 3.5 Combine like terms: -1.5 + 3.5 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 2}
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