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Simplifying 2x2 + 2x + x = 199 Reorder the terms: 2x + x + 2x2 = 199 Combine like terms: 2x + x = 3x 3x + 2x2 = 199 Solving 3x + 2x2 = 199 Solving for variable 'x'. Reorder the terms: -199 + 3x + 2x2 = 199 + -199 Combine like terms: 199 + -199 = 0 -199 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -99.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '99.5' to each side of the equation. -99.5 + 1.5x + 99.5 + x2 = 0 + 99.5 Reorder the terms: -99.5 + 99.5 + 1.5x + x2 = 0 + 99.5 Combine like terms: -99.5 + 99.5 = 0.0 0.0 + 1.5x + x2 = 0 + 99.5 1.5x + x2 = 0 + 99.5 Combine like terms: 0 + 99.5 = 99.5 1.5x + x2 = 99.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 99.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 99.5 + 0.5625 Combine like terms: 99.5 + 0.5625 = 100.0625 0.5625 + 1.5x + x2 = 100.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 100.0625 Calculate the square root of the right side: 10.003124512 Break this problem into two subproblems by setting (x + 0.75) equal to 10.003124512 and -10.003124512.Subproblem 1
x + 0.75 = 10.003124512 Simplifying x + 0.75 = 10.003124512 Reorder the terms: 0.75 + x = 10.003124512 Solving 0.75 + x = 10.003124512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 10.003124512 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 10.003124512 + -0.75 x = 10.003124512 + -0.75 Combine like terms: 10.003124512 + -0.75 = 9.253124512 x = 9.253124512 Simplifying x = 9.253124512Subproblem 2
x + 0.75 = -10.003124512 Simplifying x + 0.75 = -10.003124512 Reorder the terms: 0.75 + x = -10.003124512 Solving 0.75 + x = -10.003124512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -10.003124512 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -10.003124512 + -0.75 x = -10.003124512 + -0.75 Combine like terms: -10.003124512 + -0.75 = -10.753124512 x = -10.753124512 Simplifying x = -10.753124512Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.253124512, -10.753124512}
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