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Simplifying 24x + 10x + x2 = 9 Combine like terms: 24x + 10x = 34x 34x + x2 = 9 Solving 34x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 34x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 34x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 34x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 34x + x2 = 0 + 9 34x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 34x + x2 = 9 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = 9 + 289 Reorder the terms: 289 + 34x + x2 = 9 + 289 Combine like terms: 9 + 289 = 298 289 + 34x + x2 = 298 Factor a perfect square on the left side: (x + 17)(x + 17) = 298 Calculate the square root of the right side: 17.262676502 Break this problem into two subproblems by setting (x + 17) equal to 17.262676502 and -17.262676502.Subproblem 1
x + 17 = 17.262676502 Simplifying x + 17 = 17.262676502 Reorder the terms: 17 + x = 17.262676502 Solving 17 + x = 17.262676502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 17.262676502 + -17 Combine like terms: 17 + -17 = 0 0 + x = 17.262676502 + -17 x = 17.262676502 + -17 Combine like terms: 17.262676502 + -17 = 0.262676502 x = 0.262676502 Simplifying x = 0.262676502Subproblem 2
x + 17 = -17.262676502 Simplifying x + 17 = -17.262676502 Reorder the terms: 17 + x = -17.262676502 Solving 17 + x = -17.262676502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -17.262676502 + -17 Combine like terms: 17 + -17 = 0 0 + x = -17.262676502 + -17 x = -17.262676502 + -17 Combine like terms: -17.262676502 + -17 = -34.262676502 x = -34.262676502 Simplifying x = -34.262676502Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.262676502, -34.262676502}
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