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Simplifying x2 + 6.5x + 10.5625 = 0 Reorder the terms: 10.5625 + 6.5x + x2 = 0 Solving 10.5625 + 6.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10.5625' to each side of the equation. 10.5625 + 6.5x + -10.5625 + x2 = 0 + -10.5625 Reorder the terms: 10.5625 + -10.5625 + 6.5x + x2 = 0 + -10.5625 Combine like terms: 10.5625 + -10.5625 = 0.0000 0.0000 + 6.5x + x2 = 0 + -10.5625 6.5x + x2 = 0 + -10.5625 Combine like terms: 0 + -10.5625 = -10.5625 6.5x + x2 = -10.5625 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 = -10.5625 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -10.5625 + 10.5625 Combine like terms: -10.5625 + 10.5625 = 0.0000 10.5625 + 6.5x + x2 = 0.0000 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + 3.25) equal to 0.0000 and 0.0000.Subproblem 1
x + 3.25 = 0.0000 Simplifying x + 3.25 = 0.0000 Reorder the terms: 3.25 + x = 0.0000 Solving 3.25 + x = 0.0000 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 = 0.0000 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 0.0000 + -3.25 x = 0.0000 + -3.25 Combine like terms: 0.0000 + -3.25 = -3.25 x = -3.25 Simplifying x = -3.25Subproblem 2
x + 3.25 = 0.0000 Simplifying x + 3.25 = 0.0000 Reorder the terms: 3.25 + x = 0.0000 Solving 3.25 + x = 0.0000 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 = 0.0000 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 0.0000 + -3.25 x = 0.0000 + -3.25 Combine like terms: 0.0000 + -3.25 = -3.25 x = -3.25 Simplifying x = -3.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.25, -3.25}
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