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Simplifying 68x + -2x2 = 21x + 97 Reorder the terms: 68x + -2x2 = 97 + 21x Solving 68x + -2x2 = 97 + 21x Solving for variable 'x'. Reorder the terms: -97 + 68x + -21x + -2x2 = 97 + 21x + -97 + -21x Combine like terms: 68x + -21x = 47x -97 + 47x + -2x2 = 97 + 21x + -97 + -21x Reorder the terms: -97 + 47x + -2x2 = 97 + -97 + 21x + -21x Combine like terms: 97 + -97 = 0 -97 + 47x + -2x2 = 0 + 21x + -21x -97 + 47x + -2x2 = 21x + -21x Combine like terms: 21x + -21x = 0 -97 + 47x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 48.5 + -23.5x + x2 = 0 Move the constant term to the right: Add '-48.5' to each side of the equation. 48.5 + -23.5x + -48.5 + x2 = 0 + -48.5 Reorder the terms: 48.5 + -48.5 + -23.5x + x2 = 0 + -48.5 Combine like terms: 48.5 + -48.5 = 0.0 0.0 + -23.5x + x2 = 0 + -48.5 -23.5x + x2 = 0 + -48.5 Combine like terms: 0 + -48.5 = -48.5 -23.5x + x2 = -48.5 The x term is -23.5x. Take half its coefficient (-11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. -23.5x + 138.0625 + x2 = -48.5 + 138.0625 Reorder the terms: 138.0625 + -23.5x + x2 = -48.5 + 138.0625 Combine like terms: -48.5 + 138.0625 = 89.5625 138.0625 + -23.5x + x2 = 89.5625 Factor a perfect square on the left side: (x + -11.75)(x + -11.75) = 89.5625 Calculate the square root of the right side: 9.463746615 Break this problem into two subproblems by setting (x + -11.75) equal to 9.463746615 and -9.463746615.Subproblem 1
x + -11.75 = 9.463746615 Simplifying x + -11.75 = 9.463746615 Reorder the terms: -11.75 + x = 9.463746615 Solving -11.75 + x = 9.463746615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = 9.463746615 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = 9.463746615 + 11.75 x = 9.463746615 + 11.75 Combine like terms: 9.463746615 + 11.75 = 21.213746615 x = 21.213746615 Simplifying x = 21.213746615Subproblem 2
x + -11.75 = -9.463746615 Simplifying x + -11.75 = -9.463746615 Reorder the terms: -11.75 + x = -9.463746615 Solving -11.75 + x = -9.463746615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = -9.463746615 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = -9.463746615 + 11.75 x = -9.463746615 + 11.75 Combine like terms: -9.463746615 + 11.75 = 2.286253385 x = 2.286253385 Simplifying x = 2.286253385Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.213746615, 2.286253385}
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