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Simplifying 2x2 + 5x = 142 Reorder the terms: 5x + 2x2 = 142 Solving 5x + 2x2 = 142 Solving for variable 'x'. Reorder the terms: -142 + 5x + 2x2 = 142 + -142 Combine like terms: 142 + -142 = 0 -142 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -71 + 2.5x + x2 = 0 Move the constant term to the right: Add '71' to each side of the equation. -71 + 2.5x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + 2.5x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 2.5x + x2 = 0 + 71 2.5x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 2.5x + x2 = 71 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 = 71 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 71 + 1.5625 Combine like terms: 71 + 1.5625 = 72.5625 1.5625 + 2.5x + x2 = 72.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 72.5625 Calculate the square root of the right side: 8.518362519 Break this problem into two subproblems by setting (x + 1.25) equal to 8.518362519 and -8.518362519.Subproblem 1
x + 1.25 = 8.518362519 Simplifying x + 1.25 = 8.518362519 Reorder the terms: 1.25 + x = 8.518362519 Solving 1.25 + x = 8.518362519 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 = 8.518362519 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.518362519 + -1.25 x = 8.518362519 + -1.25 Combine like terms: 8.518362519 + -1.25 = 7.268362519 x = 7.268362519 Simplifying x = 7.268362519Subproblem 2
x + 1.25 = -8.518362519 Simplifying x + 1.25 = -8.518362519 Reorder the terms: 1.25 + x = -8.518362519 Solving 1.25 + x = -8.518362519 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 = -8.518362519 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.518362519 + -1.25 x = -8.518362519 + -1.25 Combine like terms: -8.518362519 + -1.25 = -9.768362519 x = -9.768362519 Simplifying x = -9.768362519Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.268362519, -9.768362519}
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