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Simplifying 64x2 + -75x + 21 = 0 Reorder the terms: 21 + -75x + 64x2 = 0 Solving 21 + -75x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 0.328125 + -1.171875x + x2 = 0 Move the constant term to the right: Add '-0.328125' to each side of the equation. 0.328125 + -1.171875x + -0.328125 + x2 = 0 + -0.328125 Reorder the terms: 0.328125 + -0.328125 + -1.171875x + x2 = 0 + -0.328125 Combine like terms: 0.328125 + -0.328125 = 0.000000 0.000000 + -1.171875x + x2 = 0 + -0.328125 -1.171875x + x2 = 0 + -0.328125 Combine like terms: 0 + -0.328125 = -0.328125 -1.171875x + x2 = -0.328125 The x term is -1.171875x. Take half its coefficient (-0.5859375). Square it (0.3433227539) and add it to both sides. Add '0.3433227539' to each side of the equation. -1.171875x + 0.3433227539 + x2 = -0.328125 + 0.3433227539 Reorder the terms: 0.3433227539 + -1.171875x + x2 = -0.328125 + 0.3433227539 Combine like terms: -0.328125 + 0.3433227539 = 0.0151977539 0.3433227539 + -1.171875x + x2 = 0.0151977539 Factor a perfect square on the left side: (x + -0.5859375)(x + -0.5859375) = 0.0151977539 Calculate the square root of the right side: 0.123279171 Break this problem into two subproblems by setting (x + -0.5859375) equal to 0.123279171 and -0.123279171.Subproblem 1
x + -0.5859375 = 0.123279171 Simplifying x + -0.5859375 = 0.123279171 Reorder the terms: -0.5859375 + x = 0.123279171 Solving -0.5859375 + x = 0.123279171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5859375' to each side of the equation. -0.5859375 + 0.5859375 + x = 0.123279171 + 0.5859375 Combine like terms: -0.5859375 + 0.5859375 = 0.0000000 0.0000000 + x = 0.123279171 + 0.5859375 x = 0.123279171 + 0.5859375 Combine like terms: 0.123279171 + 0.5859375 = 0.709216671 x = 0.709216671 Simplifying x = 0.709216671Subproblem 2
x + -0.5859375 = -0.123279171 Simplifying x + -0.5859375 = -0.123279171 Reorder the terms: -0.5859375 + x = -0.123279171 Solving -0.5859375 + x = -0.123279171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5859375' to each side of the equation. -0.5859375 + 0.5859375 + x = -0.123279171 + 0.5859375 Combine like terms: -0.5859375 + 0.5859375 = 0.0000000 0.0000000 + x = -0.123279171 + 0.5859375 x = -0.123279171 + 0.5859375 Combine like terms: -0.123279171 + 0.5859375 = 0.462658329 x = 0.462658329 Simplifying x = 0.462658329Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.709216671, 0.462658329}
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