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Simplifying 1 + 2x(x + -2) = 5(x + -1) Reorder the terms: 1 + 2x(-2 + x) = 5(x + -1) 1 + (-2 * 2x + x * 2x) = 5(x + -1) 1 + (-4x + 2x2) = 5(x + -1) Reorder the terms: 1 + -4x + 2x2 = 5(-1 + x) 1 + -4x + 2x2 = (-1 * 5 + x * 5) 1 + -4x + 2x2 = (-5 + 5x) Solving 1 + -4x + 2x2 = -5 + 5x Solving for variable 'x'. Reorder the terms: 1 + 5 + -4x + -5x + 2x2 = -5 + 5x + 5 + -5x Combine like terms: 1 + 5 = 6 6 + -4x + -5x + 2x2 = -5 + 5x + 5 + -5x Combine like terms: -4x + -5x = -9x 6 + -9x + 2x2 = -5 + 5x + 5 + -5x Reorder the terms: 6 + -9x + 2x2 = -5 + 5 + 5x + -5x Combine like terms: -5 + 5 = 0 6 + -9x + 2x2 = 0 + 5x + -5x 6 + -9x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 6 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -4.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.5x + x2 = 0 + -3 -4.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.5x + x2 = -3 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -3 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -3 + 5.0625 Combine like terms: -3 + 5.0625 = 2.0625 5.0625 + -4.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + -2.25) equal to 1.436140662 and -1.436140662.Subproblem 1
x + -2.25 = 1.436140662 Simplifying x + -2.25 = 1.436140662 Reorder the terms: -2.25 + x = 1.436140662 Solving -2.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.436140662 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.436140662 + 2.25 x = 1.436140662 + 2.25 Combine like terms: 1.436140662 + 2.25 = 3.686140662 x = 3.686140662 Simplifying x = 3.686140662Subproblem 2
x + -2.25 = -1.436140662 Simplifying x + -2.25 = -1.436140662 Reorder the terms: -2.25 + x = -1.436140662 Solving -2.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.436140662 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.436140662 + 2.25 x = -1.436140662 + 2.25 Combine like terms: -1.436140662 + 2.25 = 0.813859338 x = 0.813859338 Simplifying x = 0.813859338Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.686140662, 0.813859338}
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