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Simplifying 4x2 + -26x + 5 = 0 Reorder the terms: 5 + -26x + 4x2 = 0 Solving 5 + -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'. 1.25 + -6.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -6.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -6.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -6.5x + x2 = 0 + -1.25 -6.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -6.5x + x2 = -1.25 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 = -1.25 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -1.25 + 10.5625 Combine like terms: -1.25 + 10.5625 = 9.3125 10.5625 + -6.5x + x2 = 9.3125 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 9.3125 Calculate the square root of the right side: 3.051638904 Break this problem into two subproblems by setting (x + -3.25) equal to 3.051638904 and -3.051638904.Subproblem 1
x + -3.25 = 3.051638904 Simplifying x + -3.25 = 3.051638904 Reorder the terms: -3.25 + x = 3.051638904 Solving -3.25 + x = 3.051638904 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 = 3.051638904 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.051638904 + 3.25 x = 3.051638904 + 3.25 Combine like terms: 3.051638904 + 3.25 = 6.301638904 x = 6.301638904 Simplifying x = 6.301638904Subproblem 2
x + -3.25 = -3.051638904 Simplifying x + -3.25 = -3.051638904 Reorder the terms: -3.25 + x = -3.051638904 Solving -3.25 + x = -3.051638904 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 = -3.051638904 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.051638904 + 3.25 x = -3.051638904 + 3.25 Combine like terms: -3.051638904 + 3.25 = 0.198361096 x = 0.198361096 Simplifying x = 0.198361096Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.301638904, 0.198361096}
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