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Simplifying 4x2 + -20x + 100 = 83 Reorder the terms: 100 + -20x + 4x2 = 83 Solving 100 + -20x + 4x2 = 83 Solving for variable 'x'. Reorder the terms: 100 + -83 + -20x + 4x2 = 83 + -83 Combine like terms: 100 + -83 = 17 17 + -20x + 4x2 = 83 + -83 Combine like terms: 83 + -83 = 0 17 + -20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.25 + -5x + x2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + -5x + -4.25 + x2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + -5x + x2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + -5x + x2 = 0 + -4.25 -5x + x2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 -5x + x2 = -4.25 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 = -4.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.25 + 6.25 Combine like terms: -4.25 + 6.25 = 2 6.25 + -5x + x2 = 2 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -2.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -2.5 = 1.414213562 Simplifying x + -2.5 = 1.414213562 Reorder the terms: -2.5 + x = 1.414213562 Solving -2.5 + x = 1.414213562 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 = 1.414213562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.414213562 + 2.5 x = 1.414213562 + 2.5 Combine like terms: 1.414213562 + 2.5 = 3.914213562 x = 3.914213562 Simplifying x = 3.914213562Subproblem 2
x + -2.5 = -1.414213562 Simplifying x + -2.5 = -1.414213562 Reorder the terms: -2.5 + x = -1.414213562 Solving -2.5 + x = -1.414213562 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 = -1.414213562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.414213562 + 2.5 x = -1.414213562 + 2.5 Combine like terms: -1.414213562 + 2.5 = 1.085786438 x = 1.085786438 Simplifying x = 1.085786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.914213562, 1.085786438}
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