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Simplifying 3x2 + -41x = 4x2 + -7x + -24 Reorder the terms: -41x + 3x2 = 4x2 + -7x + -24 Reorder the terms: -41x + 3x2 = -24 + -7x + 4x2 Solving -41x + 3x2 = -24 + -7x + 4x2 Solving for variable 'x'. Reorder the terms: 24 + -41x + 7x + 3x2 + -4x2 = -24 + -7x + 4x2 + 24 + 7x + -4x2 Combine like terms: -41x + 7x = -34x 24 + -34x + 3x2 + -4x2 = -24 + -7x + 4x2 + 24 + 7x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 24 + -34x + -1x2 = -24 + -7x + 4x2 + 24 + 7x + -4x2 Reorder the terms: 24 + -34x + -1x2 = -24 + 24 + -7x + 7x + 4x2 + -4x2 Combine like terms: -24 + 24 = 0 24 + -34x + -1x2 = 0 + -7x + 7x + 4x2 + -4x2 24 + -34x + -1x2 = -7x + 7x + 4x2 + -4x2 Combine like terms: -7x + 7x = 0 24 + -34x + -1x2 = 0 + 4x2 + -4x2 24 + -34x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 24 + -34x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 34x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 34x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 34x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 34x + x2 = 0 + 24 34x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 34x + x2 = 24 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 = 24 + 289 Reorder the terms: 289 + 34x + x2 = 24 + 289 Combine like terms: 24 + 289 = 313 289 + 34x + x2 = 313 Factor a perfect square on the left side: (x + 17)(x + 17) = 313 Calculate the square root of the right side: 17.691806013 Break this problem into two subproblems by setting (x + 17) equal to 17.691806013 and -17.691806013.Subproblem 1
x + 17 = 17.691806013 Simplifying x + 17 = 17.691806013 Reorder the terms: 17 + x = 17.691806013 Solving 17 + x = 17.691806013 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 = 17.691806013 + -17 Combine like terms: 17 + -17 = 0 0 + x = 17.691806013 + -17 x = 17.691806013 + -17 Combine like terms: 17.691806013 + -17 = 0.691806013 x = 0.691806013 Simplifying x = 0.691806013Subproblem 2
x + 17 = -17.691806013 Simplifying x + 17 = -17.691806013 Reorder the terms: 17 + x = -17.691806013 Solving 17 + x = -17.691806013 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 = -17.691806013 + -17 Combine like terms: 17 + -17 = 0 0 + x = -17.691806013 + -17 x = -17.691806013 + -17 Combine like terms: -17.691806013 + -17 = -34.691806013 x = -34.691806013 Simplifying x = -34.691806013Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.691806013, -34.691806013}
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