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Simplifying x2 + -4x + 5 = 1.99 Reorder the terms: 5 + -4x + x2 = 1.99 Solving 5 + -4x + x2 = 1.99 Solving for variable 'x'. Reorder the terms: 5 + -1.99 + -4x + x2 = 1.99 + -1.99 Combine like terms: 5 + -1.99 = 3.01 3.01 + -4x + x2 = 1.99 + -1.99 Combine like terms: 1.99 + -1.99 = 0.00 3.01 + -4x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-3.01' to each side of the equation. 3.01 + -4x + -3.01 + x2 = 0.00 + -3.01 Reorder the terms: 3.01 + -3.01 + -4x + x2 = 0.00 + -3.01 Combine like terms: 3.01 + -3.01 = 0.00 0.00 + -4x + x2 = 0.00 + -3.01 -4x + x2 = 0.00 + -3.01 Combine like terms: 0.00 + -3.01 = -3.01 -4x + x2 = -3.01 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.01 + 4 Reorder the terms: 4 + -4x + x2 = -3.01 + 4 Combine like terms: -3.01 + 4 = 0.99 4 + -4x + x2 = 0.99 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.99 Calculate the square root of the right side: 0.994987437 Break this problem into two subproblems by setting (x + -2) equal to 0.994987437 and -0.994987437.Subproblem 1
x + -2 = 0.994987437 Simplifying x + -2 = 0.994987437 Reorder the terms: -2 + x = 0.994987437 Solving -2 + x = 0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.994987437 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.994987437 + 2 x = 0.994987437 + 2 Combine like terms: 0.994987437 + 2 = 2.994987437 x = 2.994987437 Simplifying x = 2.994987437Subproblem 2
x + -2 = -0.994987437 Simplifying x + -2 = -0.994987437 Reorder the terms: -2 + x = -0.994987437 Solving -2 + x = -0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.994987437 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.994987437 + 2 x = -0.994987437 + 2 Combine like terms: -0.994987437 + 2 = 1.005012563 x = 1.005012563 Simplifying x = 1.005012563Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.994987437, 1.005012563}
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