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Simplifying (2x2 + 5x + -17) + -1(4x + 2) = 0 Reorder the terms: (-17 + 5x + 2x2) + -1(4x + 2) = 0 Remove parenthesis around (-17 + 5x + 2x2) -17 + 5x + 2x2 + -1(4x + 2) = 0 Reorder the terms: -17 + 5x + 2x2 + -1(2 + 4x) = 0 -17 + 5x + 2x2 + (2 * -1 + 4x * -1) = 0 -17 + 5x + 2x2 + (-2 + -4x) = 0 Reorder the terms: -17 + -2 + 5x + -4x + 2x2 = 0 Combine like terms: -17 + -2 = -19 -19 + 5x + -4x + 2x2 = 0 Combine like terms: 5x + -4x = 1x -19 + 1x + 2x2 = 0 Solving -19 + 1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 0.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 0.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 0.5x + x2 = 0 + 9.5 0.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 0.5x + x2 = 9.5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 9.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 9.5 + 0.0625 Combine like terms: 9.5 + 0.0625 = 9.5625 0.0625 + 0.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + 0.25) equal to 3.092329219 and -3.092329219.Subproblem 1
x + 0.25 = 3.092329219 Simplifying x + 0.25 = 3.092329219 Reorder the terms: 0.25 + x = 3.092329219 Solving 0.25 + x = 3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.092329219 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.092329219 + -0.25 x = 3.092329219 + -0.25 Combine like terms: 3.092329219 + -0.25 = 2.842329219 x = 2.842329219 Simplifying x = 2.842329219Subproblem 2
x + 0.25 = -3.092329219 Simplifying x + 0.25 = -3.092329219 Reorder the terms: 0.25 + x = -3.092329219 Solving 0.25 + x = -3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.092329219 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.092329219 + -0.25 x = -3.092329219 + -0.25 Combine like terms: -3.092329219 + -0.25 = -3.342329219 x = -3.342329219 Simplifying x = -3.342329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.842329219, -3.342329219}
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