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Simplifying 4x2 + -26x + 9 = 0 Reorder the terms: 9 + -26x + 4x2 = 0 Solving 9 + -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'. 2.25 + -6.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -6.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -6.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -6.5x + x2 = 0 + -2.25 -6.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -6.5x + x2 = -2.25 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 = -2.25 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -2.25 + 10.5625 Combine like terms: -2.25 + 10.5625 = 8.3125 10.5625 + -6.5x + x2 = 8.3125 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 8.3125 Calculate the square root of the right side: 2.883140649 Break this problem into two subproblems by setting (x + -3.25) equal to 2.883140649 and -2.883140649.Subproblem 1
x + -3.25 = 2.883140649 Simplifying x + -3.25 = 2.883140649 Reorder the terms: -3.25 + x = 2.883140649 Solving -3.25 + x = 2.883140649 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 = 2.883140649 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.883140649 + 3.25 x = 2.883140649 + 3.25 Combine like terms: 2.883140649 + 3.25 = 6.133140649 x = 6.133140649 Simplifying x = 6.133140649Subproblem 2
x + -3.25 = -2.883140649 Simplifying x + -3.25 = -2.883140649 Reorder the terms: -3.25 + x = -2.883140649 Solving -3.25 + x = -2.883140649 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 = -2.883140649 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.883140649 + 3.25 x = -2.883140649 + 3.25 Combine like terms: -2.883140649 + 3.25 = 0.366859351 x = 0.366859351 Simplifying x = 0.366859351Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.133140649, 0.366859351}
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