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Simplifying 2.01 = (x2) + -4x + 5 2.01 = x2 + -4x + 5 Reorder the terms: 2.01 = 5 + -4x + x2 Solving 2.01 = 5 + -4x + x2 Solving for variable 'x'. Combine like terms: 2.01 + -5 = -2.99 -2.99 + 4x + -1x2 = 5 + -4x + x2 + -5 + 4x + -1x2 Reorder the terms: -2.99 + 4x + -1x2 = 5 + -5 + -4x + 4x + x2 + -1x2 Combine like terms: 5 + -5 = 0 -2.99 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2 -2.99 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -2.99 + 4x + -1x2 = 0 + x2 + -1x2 -2.99 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2.99 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2.99 + -4x + x2 = 0 Move the constant term to the right: Add '-2.99' to each side of the equation. 2.99 + -4x + -2.99 + x2 = 0 + -2.99 Reorder the terms: 2.99 + -2.99 + -4x + x2 = 0 + -2.99 Combine like terms: 2.99 + -2.99 = 0.00 0.00 + -4x + x2 = 0 + -2.99 -4x + x2 = 0 + -2.99 Combine like terms: 0 + -2.99 = -2.99 -4x + x2 = -2.99 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 = -2.99 + 4 Reorder the terms: 4 + -4x + x2 = -2.99 + 4 Combine like terms: -2.99 + 4 = 1.01 4 + -4x + x2 = 1.01 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (x + -2) equal to 1.004987562 and -1.004987562.Subproblem 1
x + -2 = 1.004987562 Simplifying x + -2 = 1.004987562 Reorder the terms: -2 + x = 1.004987562 Solving -2 + x = 1.004987562 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 = 1.004987562 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.004987562 + 2 x = 1.004987562 + 2 Combine like terms: 1.004987562 + 2 = 3.004987562 x = 3.004987562 Simplifying x = 3.004987562Subproblem 2
x + -2 = -1.004987562 Simplifying x + -2 = -1.004987562 Reorder the terms: -2 + x = -1.004987562 Solving -2 + x = -1.004987562 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 = -1.004987562 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.004987562 + 2 x = -1.004987562 + 2 Combine like terms: -1.004987562 + 2 = 0.995012438 x = 0.995012438 Simplifying x = 0.995012438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.004987562, 0.995012438}
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