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Simplifying 2x2 + 71x + -189 = 0 Reorder the terms: -189 + 71x + 2x2 = 0 Solving -189 + 71x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -94.5 + 35.5x + x2 = 0 Move the constant term to the right: Add '94.5' to each side of the equation. -94.5 + 35.5x + 94.5 + x2 = 0 + 94.5 Reorder the terms: -94.5 + 94.5 + 35.5x + x2 = 0 + 94.5 Combine like terms: -94.5 + 94.5 = 0.0 0.0 + 35.5x + x2 = 0 + 94.5 35.5x + x2 = 0 + 94.5 Combine like terms: 0 + 94.5 = 94.5 35.5x + x2 = 94.5 The x term is 35.5x. Take half its coefficient (17.75). Square it (315.0625) and add it to both sides. Add '315.0625' to each side of the equation. 35.5x + 315.0625 + x2 = 94.5 + 315.0625 Reorder the terms: 315.0625 + 35.5x + x2 = 94.5 + 315.0625 Combine like terms: 94.5 + 315.0625 = 409.5625 315.0625 + 35.5x + x2 = 409.5625 Factor a perfect square on the left side: (x + 17.75)(x + 17.75) = 409.5625 Calculate the square root of the right side: 20.237650555 Break this problem into two subproblems by setting (x + 17.75) equal to 20.237650555 and -20.237650555.Subproblem 1
x + 17.75 = 20.237650555 Simplifying x + 17.75 = 20.237650555 Reorder the terms: 17.75 + x = 20.237650555 Solving 17.75 + x = 20.237650555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.75' to each side of the equation. 17.75 + -17.75 + x = 20.237650555 + -17.75 Combine like terms: 17.75 + -17.75 = 0.00 0.00 + x = 20.237650555 + -17.75 x = 20.237650555 + -17.75 Combine like terms: 20.237650555 + -17.75 = 2.487650555 x = 2.487650555 Simplifying x = 2.487650555Subproblem 2
x + 17.75 = -20.237650555 Simplifying x + 17.75 = -20.237650555 Reorder the terms: 17.75 + x = -20.237650555 Solving 17.75 + x = -20.237650555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.75' to each side of the equation. 17.75 + -17.75 + x = -20.237650555 + -17.75 Combine like terms: 17.75 + -17.75 = 0.00 0.00 + x = -20.237650555 + -17.75 x = -20.237650555 + -17.75 Combine like terms: -20.237650555 + -17.75 = -37.987650555 x = -37.987650555 Simplifying x = -37.987650555Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.487650555, -37.987650555}
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