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Simplifying 100 + -10x + 0.1x2 = 500 Solving 100 + -10x + 0.1x2 = 500 Solving for variable 'x'. Reorder the terms: 100 + -500 + -10x + 0.1x2 = 500 + -500 Combine like terms: 100 + -500 = -400 -400 + -10x + 0.1x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -400 + -10x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -4000 + -100x + x2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + -100x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + -100x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + -100x + x2 = 0 + 4000 -100x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 -100x + x2 = 4000 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 = 4000 + 2500 Reorder the terms: 2500 + -100x + x2 = 4000 + 2500 Combine like terms: 4000 + 2500 = 6500 2500 + -100x + x2 = 6500 Factor a perfect square on the left side: (x + -50)(x + -50) = 6500 Calculate the square root of the right side: 80.622577483 Break this problem into two subproblems by setting (x + -50) equal to 80.622577483 and -80.622577483.Subproblem 1
x + -50 = 80.622577483 Simplifying x + -50 = 80.622577483 Reorder the terms: -50 + x = 80.622577483 Solving -50 + x = 80.622577483 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 = 80.622577483 + 50 Combine like terms: -50 + 50 = 0 0 + x = 80.622577483 + 50 x = 80.622577483 + 50 Combine like terms: 80.622577483 + 50 = 130.622577483 x = 130.622577483 Simplifying x = 130.622577483Subproblem 2
x + -50 = -80.622577483 Simplifying x + -50 = -80.622577483 Reorder the terms: -50 + x = -80.622577483 Solving -50 + x = -80.622577483 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 = -80.622577483 + 50 Combine like terms: -50 + 50 = 0 0 + x = -80.622577483 + 50 x = -80.622577483 + 50 Combine like terms: -80.622577483 + 50 = -30.622577483 x = -30.622577483 Simplifying x = -30.622577483Solution
The solution to the problem is based on the solutions from the subproblems. x = {130.622577483, -30.622577483}
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