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Simplifying 2x2 + 5x = 128 Reorder the terms: 5x + 2x2 = 128 Solving 5x + 2x2 = 128 Solving for variable 'x'. Reorder the terms: -128 + 5x + 2x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -128 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -64 + 2.5x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 2.5x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 2.5x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 2.5x + x2 = 0 + 64 2.5x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 2.5x + x2 = 64 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 64 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 64 + 1.5625 Combine like terms: 64 + 1.5625 = 65.5625 1.5625 + 2.5x + x2 = 65.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 65.5625 Calculate the square root of the right side: 8.09706737 Break this problem into two subproblems by setting (x + 1.25) equal to 8.09706737 and -8.09706737.Subproblem 1
x + 1.25 = 8.09706737 Simplifying x + 1.25 = 8.09706737 Reorder the terms: 1.25 + x = 8.09706737 Solving 1.25 + x = 8.09706737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 8.09706737 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.09706737 + -1.25 x = 8.09706737 + -1.25 Combine like terms: 8.09706737 + -1.25 = 6.84706737 x = 6.84706737 Simplifying x = 6.84706737Subproblem 2
x + 1.25 = -8.09706737 Simplifying x + 1.25 = -8.09706737 Reorder the terms: 1.25 + x = -8.09706737 Solving 1.25 + x = -8.09706737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -8.09706737 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.09706737 + -1.25 x = -8.09706737 + -1.25 Combine like terms: -8.09706737 + -1.25 = -9.34706737 x = -9.34706737 Simplifying x = -9.34706737Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.84706737, -9.34706737}
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