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Simplifying 2x2 + -25x + 76 = 0 Reorder the terms: 76 + -25x + 2x2 = 0 Solving 76 + -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'. 38 + -12.5x + x2 = 0 Move the constant term to the right: Add '-38' to each side of the equation. 38 + -12.5x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + -12.5x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -12.5x + x2 = 0 + -38 -12.5x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 -12.5x + x2 = -38 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 = -38 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -38 + 39.0625 Combine like terms: -38 + 39.0625 = 1.0625 39.0625 + -12.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + -6.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + -6.25 = 1.030776406 Simplifying x + -6.25 = 1.030776406 Reorder the terms: -6.25 + x = 1.030776406 Solving -6.25 + x = 1.030776406 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 = 1.030776406 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 1.030776406 + 6.25 x = 1.030776406 + 6.25 Combine like terms: 1.030776406 + 6.25 = 7.280776406 x = 7.280776406 Simplifying x = 7.280776406Subproblem 2
x + -6.25 = -1.030776406 Simplifying x + -6.25 = -1.030776406 Reorder the terms: -6.25 + x = -1.030776406 Solving -6.25 + x = -1.030776406 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 = -1.030776406 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -1.030776406 + 6.25 x = -1.030776406 + 6.25 Combine like terms: -1.030776406 + 6.25 = 5.219223594 x = 5.219223594 Simplifying x = 5.219223594Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.280776406, 5.219223594}
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