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Simplifying 900 + -0.25x2 = 100 + 10x Solving 900 + -0.25x2 = 100 + 10x Solving for variable 'x'. Reorder the terms: 900 + -100 + -10x + -0.25x2 = 100 + 10x + -100 + -10x Combine like terms: 900 + -100 = 800 800 + -10x + -0.25x2 = 100 + 10x + -100 + -10x Reorder the terms: 800 + -10x + -0.25x2 = 100 + -100 + 10x + -10x Combine like terms: 100 + -100 = 0 800 + -10x + -0.25x2 = 0 + 10x + -10x 800 + -10x + -0.25x2 = 10x + -10x Combine like terms: 10x + -10x = 0 800 + -10x + -0.25x2 = 0 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -3200 + 40x + x2 = 0 Move the constant term to the right: Add '3200' to each side of the equation. -3200 + 40x + 3200 + x2 = 0 + 3200 Reorder the terms: -3200 + 3200 + 40x + x2 = 0 + 3200 Combine like terms: -3200 + 3200 = 0 0 + 40x + x2 = 0 + 3200 40x + x2 = 0 + 3200 Combine like terms: 0 + 3200 = 3200 40x + x2 = 3200 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 = 3200 + 400 Reorder the terms: 400 + 40x + x2 = 3200 + 400 Combine like terms: 3200 + 400 = 3600 400 + 40x + x2 = 3600 Factor a perfect square on the left side: (x + 20)(x + 20) = 3600 Calculate the square root of the right side: 60 Break this problem into two subproblems by setting (x + 20) equal to 60 and -60.Subproblem 1
x + 20 = 60 Simplifying x + 20 = 60 Reorder the terms: 20 + x = 60 Solving 20 + x = 60 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 = 60 + -20 Combine like terms: 20 + -20 = 0 0 + x = 60 + -20 x = 60 + -20 Combine like terms: 60 + -20 = 40 x = 40 Simplifying x = 40Subproblem 2
x + 20 = -60 Simplifying x + 20 = -60 Reorder the terms: 20 + x = -60 Solving 20 + x = -60 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 = -60 + -20 Combine like terms: 20 + -20 = 0 0 + x = -60 + -20 x = -60 + -20 Combine like terms: -60 + -20 = -80 x = -80 Simplifying x = -80Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, -80}
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