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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 = 12.8125 10.5625 + 6.5x + x2 = 12.8125 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 12.8125 Calculate the square root of the right side: 3.579455266 Break this problem into two subproblems by setting (x + 3.25) equal to 3.579455266 and -3.579455266.Subproblem 1
x + 3.25 = 3.579455266 Simplifying x + 3.25 = 3.579455266 Reorder the terms: 3.25 + x = 3.579455266 Solving 3.25 + x = 3.579455266 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 = 3.579455266 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.579455266 + -3.25 x = 3.579455266 + -3.25 Combine like terms: 3.579455266 + -3.25 = 0.329455266 x = 0.329455266 Simplifying x = 0.329455266Subproblem 2
x + 3.25 = -3.579455266 Simplifying x + 3.25 = -3.579455266 Reorder the terms: 3.25 + x = -3.579455266 Solving 3.25 + x = -3.579455266 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 = -3.579455266 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.579455266 + -3.25 x = -3.579455266 + -3.25 Combine like terms: -3.579455266 + -3.25 = -6.829455266 x = -6.829455266 Simplifying x = -6.829455266Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.329455266, -6.829455266}
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