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Simplifying 2x2 + -25x + 36 = 0 Reorder the terms: 36 + -25x + 2x2 = 0 Solving 36 + -25x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18 + -12.5x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -12.5x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -12.5x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -12.5x + x2 = 0 + -18 -12.5x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -12.5x + x2 = -18 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -18 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -18 + 39.0625 Combine like terms: -18 + 39.0625 = 21.0625 39.0625 + -12.5x + x2 = 21.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (x + -6.25) equal to 4.589389938 and -4.589389938.Subproblem 1
x + -6.25 = 4.589389938 Simplifying x + -6.25 = 4.589389938 Reorder the terms: -6.25 + x = 4.589389938 Solving -6.25 + x = 4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 4.589389938 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 4.589389938 + 6.25 x = 4.589389938 + 6.25 Combine like terms: 4.589389938 + 6.25 = 10.839389938 x = 10.839389938 Simplifying x = 10.839389938Subproblem 2
x + -6.25 = -4.589389938 Simplifying x + -6.25 = -4.589389938 Reorder the terms: -6.25 + x = -4.589389938 Solving -6.25 + x = -4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -4.589389938 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -4.589389938 + 6.25 x = -4.589389938 + 6.25 Combine like terms: -4.589389938 + 6.25 = 1.660610062 x = 1.660610062 Simplifying x = 1.660610062Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.839389938, 1.660610062}
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