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Simplifying 2x2 + 5x = 144 Reorder the terms: 5x + 2x2 = 144 Solving 5x + 2x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 5x + 2x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -72 + 2.5x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + 2.5x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 2.5x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 2.5x + x2 = 0 + 72 2.5x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 2.5x + x2 = 72 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 = 72 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 72 + 1.5625 Combine like terms: 72 + 1.5625 = 73.5625 1.5625 + 2.5x + x2 = 73.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 73.5625 Calculate the square root of the right side: 8.576858399 Break this problem into two subproblems by setting (x + 1.25) equal to 8.576858399 and -8.576858399.Subproblem 1
x + 1.25 = 8.576858399 Simplifying x + 1.25 = 8.576858399 Reorder the terms: 1.25 + x = 8.576858399 Solving 1.25 + x = 8.576858399 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 = 8.576858399 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.576858399 + -1.25 x = 8.576858399 + -1.25 Combine like terms: 8.576858399 + -1.25 = 7.326858399 x = 7.326858399 Simplifying x = 7.326858399Subproblem 2
x + 1.25 = -8.576858399 Simplifying x + 1.25 = -8.576858399 Reorder the terms: 1.25 + x = -8.576858399 Solving 1.25 + x = -8.576858399 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 = -8.576858399 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.576858399 + -1.25 x = -8.576858399 + -1.25 Combine like terms: -8.576858399 + -1.25 = -9.826858399 x = -9.826858399 Simplifying x = -9.826858399Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.326858399, -9.826858399}
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