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Simplifying 4x2 + 20x + 100 = 101 Reorder the terms: 100 + 20x + 4x2 = 101 Solving 100 + 20x + 4x2 = 101 Solving for variable 'x'. Reorder the terms: 100 + -101 + 20x + 4x2 = 101 + -101 Combine like terms: 100 + -101 = -1 -1 + 20x + 4x2 = 101 + -101 Combine like terms: 101 + -101 = 0 -1 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 5x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 5x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 5x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 5x + x2 = 0 + 0.25 5x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 5x + x2 = 0.25 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.25 + 6.25 Combine like terms: 0.25 + 6.25 = 6.5 6.25 + 5x + x2 = 6.5 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + 2.5) equal to 2.549509757 and -2.549509757.Subproblem 1
x + 2.5 = 2.549509757 Simplifying x + 2.5 = 2.549509757 Reorder the terms: 2.5 + x = 2.549509757 Solving 2.5 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.549509757 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.549509757 + -2.5 x = 2.549509757 + -2.5 Combine like terms: 2.549509757 + -2.5 = 0.049509757 x = 0.049509757 Simplifying x = 0.049509757Subproblem 2
x + 2.5 = -2.549509757 Simplifying x + 2.5 = -2.549509757 Reorder the terms: 2.5 + x = -2.549509757 Solving 2.5 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.549509757 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.549509757 + -2.5 x = -2.549509757 + -2.5 Combine like terms: -2.549509757 + -2.5 = -5.049509757 x = -5.049509757 Simplifying x = -5.049509757Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.049509757, -5.049509757}
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