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Simplifying 4x2 + -34x + 49 = 0 Reorder the terms: 49 + -34x + 4x2 = 0 Solving 49 + -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'. 12.25 + -8.5x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + -8.5x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + -8.5x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + -8.5x + x2 = 0 + -12.25 -8.5x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 -8.5x + x2 = -12.25 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 = -12.25 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -12.25 + 18.0625 Combine like terms: -12.25 + 18.0625 = 5.8125 18.0625 + -8.5x + x2 = 5.8125 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 5.8125 Calculate the square root of the right side: 2.41091269 Break this problem into two subproblems by setting (x + -4.25) equal to 2.41091269 and -2.41091269.Subproblem 1
x + -4.25 = 2.41091269 Simplifying x + -4.25 = 2.41091269 Reorder the terms: -4.25 + x = 2.41091269 Solving -4.25 + x = 2.41091269 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 = 2.41091269 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 2.41091269 + 4.25 x = 2.41091269 + 4.25 Combine like terms: 2.41091269 + 4.25 = 6.66091269 x = 6.66091269 Simplifying x = 6.66091269Subproblem 2
x + -4.25 = -2.41091269 Simplifying x + -4.25 = -2.41091269 Reorder the terms: -4.25 + x = -2.41091269 Solving -4.25 + x = -2.41091269 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 = -2.41091269 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -2.41091269 + 4.25 x = -2.41091269 + 4.25 Combine like terms: -2.41091269 + 4.25 = 1.83908731 x = 1.83908731 Simplifying x = 1.83908731Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.66091269, 1.83908731}
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