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Simplifying x2 + -6.5x + 0.64 = 0 Reorder the terms: 0.64 + -6.5x + x2 = 0 Solving 0.64 + -6.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.64' to each side of the equation. 0.64 + -6.5x + -0.64 + x2 = 0 + -0.64 Reorder the terms: 0.64 + -0.64 + -6.5x + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + -6.5x + x2 = 0 + -0.64 -6.5x + x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 -6.5x + x2 = -0.64 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 = -0.64 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -0.64 + 10.5625 Combine like terms: -0.64 + 10.5625 = 9.9225 10.5625 + -6.5x + x2 = 9.9225 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 9.9225 Calculate the square root of the right side: 3.15 Break this problem into two subproblems by setting (x + -3.25) equal to 3.15 and -3.15.Subproblem 1
x + -3.25 = 3.15 Simplifying x + -3.25 = 3.15 Reorder the terms: -3.25 + x = 3.15 Solving -3.25 + x = 3.15 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 = 3.15 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.15 + 3.25 x = 3.15 + 3.25 Combine like terms: 3.15 + 3.25 = 6.4 x = 6.4 Simplifying x = 6.4Subproblem 2
x + -3.25 = -3.15 Simplifying x + -3.25 = -3.15 Reorder the terms: -3.25 + x = -3.15 Solving -3.25 + x = -3.15 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 = -3.15 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.15 + 3.25 x = -3.15 + 3.25 Combine like terms: -3.15 + 3.25 = 0.1 x = 0.1 Simplifying x = 0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.4, 0.1}
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