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Simplifying (0.5x + -10)(0.5x + -10) = 0 Reorder the terms: (-10 + 0.5x)(0.5x + -10) = 0 Reorder the terms: (-10 + 0.5x)(-10 + 0.5x) = 0 Multiply (-10 + 0.5x) * (-10 + 0.5x) (-10(-10 + 0.5x) + 0.5x * (-10 + 0.5x)) = 0 ((-10 * -10 + 0.5x * -10) + 0.5x * (-10 + 0.5x)) = 0 ((100 + -5x) + 0.5x * (-10 + 0.5x)) = 0 (100 + -5x + (-10 * 0.5x + 0.5x * 0.5x)) = 0 (100 + -5x + (-5x + 0.25x2)) = 0 Combine like terms: -5x + -5x = -10x (100 + -10x + 0.25x2) = 0 Solving 100 + -10x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 400 + -40x + x2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -40x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -40x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -40x + x2 = 0 + -400 -40x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -40x + x2 = -400 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -400 + 400 Reorder the terms: 400 + -40x + x2 = -400 + 400 Combine like terms: -400 + 400 = 0 400 + -40x + x2 = 0 Factor a perfect square on the left side: (x + -20)(x + -20) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -20) equal to 0 and 0.Subproblem 1
x + -20 = 0 Simplifying x + -20 = 0 Reorder the terms: -20 + x = 0 Solving -20 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + x = 0 + 20 x = 0 + 20 Combine like terms: 0 + 20 = 20 x = 20 Simplifying x = 20Subproblem 2
x + -20 = 0 Simplifying x + -20 = 0 Reorder the terms: -20 + x = 0 Solving -20 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + x = 0 + 20 x = 0 + 20 Combine like terms: 0 + 20 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, 20}
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