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Simplifying 4x2 + -26x + 19 = 0 Reorder the terms: 19 + -26x + 4x2 = 0 Solving 19 + -26x + 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'. 4.75 + -6.5x + x2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + -6.5x + -4.75 + x2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + -6.5x + x2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + -6.5x + x2 = 0 + -4.75 -6.5x + x2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 -6.5x + x2 = -4.75 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -4.75 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -4.75 + 10.5625 Combine like terms: -4.75 + 10.5625 = 5.8125 10.5625 + -6.5x + x2 = 5.8125 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 5.8125 Calculate the square root of the right side: 2.41091269 Break this problem into two subproblems by setting (x + -3.25) equal to 2.41091269 and -2.41091269.Subproblem 1
x + -3.25 = 2.41091269 Simplifying x + -3.25 = 2.41091269 Reorder the terms: -3.25 + x = 2.41091269 Solving -3.25 + x = 2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.41091269 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.41091269 + 3.25 x = 2.41091269 + 3.25 Combine like terms: 2.41091269 + 3.25 = 5.66091269 x = 5.66091269 Simplifying x = 5.66091269Subproblem 2
x + -3.25 = -2.41091269 Simplifying x + -3.25 = -2.41091269 Reorder the terms: -3.25 + x = -2.41091269 Solving -3.25 + x = -2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.41091269 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.41091269 + 3.25 x = -2.41091269 + 3.25 Combine like terms: -2.41091269 + 3.25 = 0.83908731 x = 0.83908731 Simplifying x = 0.83908731Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.66091269, 0.83908731}
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