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Simplifying 100 = 46x + x2 Solving 100 = 46x + x2 Solving for variable 'x'. Reorder the terms: 100 + -46x + -1x2 = 46x + -46x + x2 + -1x2 Combine like terms: 46x + -46x = 0 100 + -46x + -1x2 = 0 + x2 + -1x2 100 + -46x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 100 + -46x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 46x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 46x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 46x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 46x + x2 = 0 + 100 46x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 46x + x2 = 100 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = 100 + 529 Reorder the terms: 529 + 46x + x2 = 100 + 529 Combine like terms: 100 + 529 = 629 529 + 46x + x2 = 629 Factor a perfect square on the left side: (x + 23)(x + 23) = 629 Calculate the square root of the right side: 25.079872408 Break this problem into two subproblems by setting (x + 23) equal to 25.079872408 and -25.079872408.Subproblem 1
x + 23 = 25.079872408 Simplifying x + 23 = 25.079872408 Reorder the terms: 23 + x = 25.079872408 Solving 23 + x = 25.079872408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 25.079872408 + -23 Combine like terms: 23 + -23 = 0 0 + x = 25.079872408 + -23 x = 25.079872408 + -23 Combine like terms: 25.079872408 + -23 = 2.079872408 x = 2.079872408 Simplifying x = 2.079872408Subproblem 2
x + 23 = -25.079872408 Simplifying x + 23 = -25.079872408 Reorder the terms: 23 + x = -25.079872408 Solving 23 + x = -25.079872408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -25.079872408 + -23 Combine like terms: 23 + -23 = 0 0 + x = -25.079872408 + -23 x = -25.079872408 + -23 Combine like terms: -25.079872408 + -23 = -48.079872408 x = -48.079872408 Simplifying x = -48.079872408Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.079872408, -48.079872408}
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