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Simplifying -5x2 + 5x + 17 = 0 Reorder the terms: 17 + 5x + -5x2 = 0 Solving 17 + 5x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.4 + -1x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -1x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -1x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -1x + x2 = 0 + 3.4 -1x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -1x + x2 = 3.4 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3.4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.4 + 0.25 Combine like terms: 3.4 + 0.25 = 3.65 0.25 + -1x + x2 = 3.65 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.65 Calculate the square root of the right side: 1.910497317 Break this problem into two subproblems by setting (x + -0.5) equal to 1.910497317 and -1.910497317.Subproblem 1
x + -0.5 = 1.910497317 Simplifying x + -0.5 = 1.910497317 Reorder the terms: -0.5 + x = 1.910497317 Solving -0.5 + x = 1.910497317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.910497317 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.910497317 + 0.5 x = 1.910497317 + 0.5 Combine like terms: 1.910497317 + 0.5 = 2.410497317 x = 2.410497317 Simplifying x = 2.410497317Subproblem 2
x + -0.5 = -1.910497317 Simplifying x + -0.5 = -1.910497317 Reorder the terms: -0.5 + x = -1.910497317 Solving -0.5 + x = -1.910497317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.910497317 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.910497317 + 0.5 x = -1.910497317 + 0.5 Combine like terms: -1.910497317 + 0.5 = -1.410497317 x = -1.410497317 Simplifying x = -1.410497317Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.410497317, -1.410497317}
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