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Simplifying (-0.5x + 0.9)(x + -0.2) = 0 Reorder the terms: (0.9 + -0.5x)(x + -0.2) = 0 Reorder the terms: (0.9 + -0.5x)(-0.2 + x) = 0 Multiply (0.9 + -0.5x) * (-0.2 + x) (0.9(-0.2 + x) + -0.5x * (-0.2 + x)) = 0 ((-0.2 * 0.9 + x * 0.9) + -0.5x * (-0.2 + x)) = 0 ((-0.18 + 0.9x) + -0.5x * (-0.2 + x)) = 0 (-0.18 + 0.9x + (-0.2 * -0.5x + x * -0.5x)) = 0 (-0.18 + 0.9x + (0.1x + -0.5x2)) = 0 Combine like terms: 0.9x + 0.1x = 1x (-0.18 + 1x + -0.5x2) = 0 Solving -0.18 + 1x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 0.36 + -2x + x2 = 0 Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + -2x + -0.36 + x2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + -2x + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + -2x + x2 = 0 + -0.36 -2x + x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 -2x + x2 = -0.36 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.36 + 1 Reorder the terms: 1 + -2x + x2 = -0.36 + 1 Combine like terms: -0.36 + 1 = 0.64 1 + -2x + x2 = 0.64 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.64 Calculate the square root of the right side: 0.8 Break this problem into two subproblems by setting (x + -1) equal to 0.8 and -0.8.Subproblem 1
x + -1 = 0.8 Simplifying x + -1 = 0.8 Reorder the terms: -1 + x = 0.8 Solving -1 + x = 0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.8 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.8 + 1 x = 0.8 + 1 Combine like terms: 0.8 + 1 = 1.8 x = 1.8 Simplifying x = 1.8Subproblem 2
x + -1 = -0.8 Simplifying x + -1 = -0.8 Reorder the terms: -1 + x = -0.8 Solving -1 + x = -0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.8 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.8 + 1 x = -0.8 + 1 Combine like terms: -0.8 + 1 = 0.2 x = 0.2 Simplifying x = 0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8, 0.2}
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