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Simplifying -4x2 + 26x + 11 = 0 Reorder the terms: 11 + 26x + -4x2 = 0 Solving 11 + 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'. -2.75 + -6.5x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -6.5x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -6.5x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -6.5x + x2 = 0 + 2.75 -6.5x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -6.5x + x2 = 2.75 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 = 2.75 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 2.75 + 10.5625 Combine like terms: 2.75 + 10.5625 = 13.3125 10.5625 + -6.5x + x2 = 13.3125 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 13.3125 Calculate the square root of the right side: 3.64862988 Break this problem into two subproblems by setting (x + -3.25) equal to 3.64862988 and -3.64862988.Subproblem 1
x + -3.25 = 3.64862988 Simplifying x + -3.25 = 3.64862988 Reorder the terms: -3.25 + x = 3.64862988 Solving -3.25 + x = 3.64862988 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 = 3.64862988 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.64862988 + 3.25 x = 3.64862988 + 3.25 Combine like terms: 3.64862988 + 3.25 = 6.89862988 x = 6.89862988 Simplifying x = 6.89862988Subproblem 2
x + -3.25 = -3.64862988 Simplifying x + -3.25 = -3.64862988 Reorder the terms: -3.25 + x = -3.64862988 Solving -3.25 + x = -3.64862988 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 = -3.64862988 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.64862988 + 3.25 x = -3.64862988 + 3.25 Combine like terms: -3.64862988 + 3.25 = -0.39862988 x = -0.39862988 Simplifying x = -0.39862988Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.89862988, -0.39862988}
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