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Simplifying 2x2 + 10x = 99 Reorder the terms: 10x + 2x2 = 99 Solving 10x + 2x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + 10x + 2x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -49.5 + 5x + x2 = 0 Move the constant term to the right: Add '49.5' to each side of the equation. -49.5 + 5x + 49.5 + x2 = 0 + 49.5 Reorder the terms: -49.5 + 49.5 + 5x + x2 = 0 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + 5x + x2 = 0 + 49.5 5x + x2 = 0 + 49.5 Combine like terms: 0 + 49.5 = 49.5 5x + x2 = 49.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 49.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 49.5 + 6.25 Combine like terms: 49.5 + 6.25 = 55.75 6.25 + 5x + x2 = 55.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 55.75 Calculate the square root of the right side: 7.466592262 Break this problem into two subproblems by setting (x + 2.5) equal to 7.466592262 and -7.466592262.Subproblem 1
x + 2.5 = 7.466592262 Simplifying x + 2.5 = 7.466592262 Reorder the terms: 2.5 + x = 7.466592262 Solving 2.5 + x = 7.466592262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.466592262 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.466592262 + -2.5 x = 7.466592262 + -2.5 Combine like terms: 7.466592262 + -2.5 = 4.966592262 x = 4.966592262 Simplifying x = 4.966592262Subproblem 2
x + 2.5 = -7.466592262 Simplifying x + 2.5 = -7.466592262 Reorder the terms: 2.5 + x = -7.466592262 Solving 2.5 + x = -7.466592262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.466592262 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.466592262 + -2.5 x = -7.466592262 + -2.5 Combine like terms: -7.466592262 + -2.5 = -9.966592262 x = -9.966592262 Simplifying x = -9.966592262Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.966592262, -9.966592262}
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