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Simplifying (0.2x + -10)(0.2x + -10) = 0 Reorder the terms: (-10 + 0.2x)(0.2x + -10) = 0 Reorder the terms: (-10 + 0.2x)(-10 + 0.2x) = 0 Multiply (-10 + 0.2x) * (-10 + 0.2x) (-10(-10 + 0.2x) + 0.2x * (-10 + 0.2x)) = 0 ((-10 * -10 + 0.2x * -10) + 0.2x * (-10 + 0.2x)) = 0 ((100 + -2x) + 0.2x * (-10 + 0.2x)) = 0 (100 + -2x + (-10 * 0.2x + 0.2x * 0.2x)) = 0 (100 + -2x + (-2x + 0.04x2)) = 0 Combine like terms: -2x + -2x = -4x (100 + -4x + 0.04x2) = 0 Solving 100 + -4x + 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'. 2500 + -100x + x2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -100x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -100x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -100x + x2 = 0 + -2500 -100x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -100x + x2 = -2500 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -2500 + 2500 Reorder the terms: 2500 + -100x + x2 = -2500 + 2500 Combine like terms: -2500 + 2500 = 0 2500 + -100x + x2 = 0 Factor a perfect square on the left side: (x + -50)(x + -50) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -50) equal to 0 and 0.Subproblem 1
x + -50 = 0 Simplifying x + -50 = 0 Reorder the terms: -50 + x = 0 Solving -50 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + x = 0 + 50 x = 0 + 50 Combine like terms: 0 + 50 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -50 = 0 Simplifying x + -50 = 0 Reorder the terms: -50 + x = 0 Solving -50 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + x = 0 + 50 x = 0 + 50 Combine like terms: 0 + 50 = 50 x = 50 Simplifying x = 50Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, 50}
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