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Simplifying 4x2 + -34x + -35 = 0 Reorder the terms: -35 + -34x + 4x2 = 0 Solving -35 + -34x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + -8.5x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -8.5x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -8.5x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -8.5x + x2 = 0 + 8.75 -8.5x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -8.5x + x2 = 8.75 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 8.75 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 8.75 + 18.0625 Combine like terms: 8.75 + 18.0625 = 26.8125 18.0625 + -8.5x + x2 = 26.8125 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 26.8125 Calculate the square root of the right side: 5.178078794 Break this problem into two subproblems by setting (x + -4.25) equal to 5.178078794 and -5.178078794.Subproblem 1
x + -4.25 = 5.178078794 Simplifying x + -4.25 = 5.178078794 Reorder the terms: -4.25 + x = 5.178078794 Solving -4.25 + x = 5.178078794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 5.178078794 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 5.178078794 + 4.25 x = 5.178078794 + 4.25 Combine like terms: 5.178078794 + 4.25 = 9.428078794 x = 9.428078794 Simplifying x = 9.428078794Subproblem 2
x + -4.25 = -5.178078794 Simplifying x + -4.25 = -5.178078794 Reorder the terms: -4.25 + x = -5.178078794 Solving -4.25 + x = -5.178078794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -5.178078794 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -5.178078794 + 4.25 x = -5.178078794 + 4.25 Combine like terms: -5.178078794 + 4.25 = -0.928078794 x = -0.928078794 Simplifying x = -0.928078794Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.428078794, -0.928078794}
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