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Simplifying 2x2 + 5x = 196 Reorder the terms: 5x + 2x2 = 196 Solving 5x + 2x2 = 196 Solving for variable 'x'. Reorder the terms: -196 + 5x + 2x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -196 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -98 + 2.5x + x2 = 0 Move the constant term to the right: Add '98' to each side of the equation. -98 + 2.5x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 2.5x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 2.5x + x2 = 0 + 98 2.5x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 2.5x + x2 = 98 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 = 98 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 98 + 1.5625 Combine like terms: 98 + 1.5625 = 99.5625 1.5625 + 2.5x + x2 = 99.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 99.5625 Calculate the square root of the right side: 9.978101022 Break this problem into two subproblems by setting (x + 1.25) equal to 9.978101022 and -9.978101022.Subproblem 1
x + 1.25 = 9.978101022 Simplifying x + 1.25 = 9.978101022 Reorder the terms: 1.25 + x = 9.978101022 Solving 1.25 + x = 9.978101022 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 = 9.978101022 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 9.978101022 + -1.25 x = 9.978101022 + -1.25 Combine like terms: 9.978101022 + -1.25 = 8.728101022 x = 8.728101022 Simplifying x = 8.728101022Subproblem 2
x + 1.25 = -9.978101022 Simplifying x + 1.25 = -9.978101022 Reorder the terms: 1.25 + x = -9.978101022 Solving 1.25 + x = -9.978101022 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 = -9.978101022 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -9.978101022 + -1.25 x = -9.978101022 + -1.25 Combine like terms: -9.978101022 + -1.25 = -11.228101022 x = -11.228101022 Simplifying x = -11.228101022Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.728101022, -11.228101022}
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