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Simplifying 0.52(0.50 + -1x)(0.045 + -1x) = 0 Multiply (0.50 + -1x) * (0.045 + -1x) 0.52(0.50(0.045 + -1x) + -1x * (0.045 + -1x)) = 0 0.52((0.045 * 0.50 + -1x * 0.50) + -1x * (0.045 + -1x)) = 0 0.52((0.0225 + -0.5x) + -1x * (0.045 + -1x)) = 0 0.52(0.0225 + -0.5x + (0.045 * -1x + -1x * -1x)) = 0 0.52(0.0225 + -0.5x + (-0.045x + 1x2)) = 0 Combine like terms: -0.5x + -0.045x = -0.545x 0.52(0.0225 + -0.545x + 1x2) = 0 (0.0225 * 0.52 + -0.545x * 0.52 + 1x2 * 0.52) = 0 (0.0117 + -0.2834x + 0.52x2) = 0 Solving 0.0117 + -0.2834x + 0.52x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.52 the coefficient of the squared term: Divide each side by '0.52'. 0.0225 + -0.545x + x2 = 0 Move the constant term to the right: Add '-0.0225' to each side of the equation. 0.0225 + -0.545x + -0.0225 + x2 = 0 + -0.0225 Reorder the terms: 0.0225 + -0.0225 + -0.545x + x2 = 0 + -0.0225 Combine like terms: 0.0225 + -0.0225 = 0.0000 0.0000 + -0.545x + x2 = 0 + -0.0225 -0.545x + x2 = 0 + -0.0225 Combine like terms: 0 + -0.0225 = -0.0225 -0.545x + x2 = -0.0225 The x term is -0.545x. Take half its coefficient (-0.2725). Square it (0.07425625) and add it to both sides. Add '0.07425625' to each side of the equation. -0.545x + 0.07425625 + x2 = -0.0225 + 0.07425625 Reorder the terms: 0.07425625 + -0.545x + x2 = -0.0225 + 0.07425625 Combine like terms: -0.0225 + 0.07425625 = 0.05175625 0.07425625 + -0.545x + x2 = 0.05175625 Factor a perfect square on the left side: (x + -0.2725)(x + -0.2725) = 0.05175625 Calculate the square root of the right side: 0.2275 Break this problem into two subproblems by setting (x + -0.2725) equal to 0.2275 and -0.2275.Subproblem 1
x + -0.2725 = 0.2275 Simplifying x + -0.2725 = 0.2275 Reorder the terms: -0.2725 + x = 0.2275 Solving -0.2725 + x = 0.2275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2725' to each side of the equation. -0.2725 + 0.2725 + x = 0.2275 + 0.2725 Combine like terms: -0.2725 + 0.2725 = 0.0000 0.0000 + x = 0.2275 + 0.2725 x = 0.2275 + 0.2725 Combine like terms: 0.2275 + 0.2725 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + -0.2725 = -0.2275 Simplifying x + -0.2725 = -0.2275 Reorder the terms: -0.2725 + x = -0.2275 Solving -0.2725 + x = -0.2275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2725' to each side of the equation. -0.2725 + 0.2725 + x = -0.2275 + 0.2725 Combine like terms: -0.2725 + 0.2725 = 0.0000 0.0000 + x = -0.2275 + 0.2725 x = -0.2275 + 0.2725 Combine like terms: -0.2275 + 0.2725 = 0.045 x = 0.045 Simplifying x = 0.045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, 0.045}
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