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Simplifying 24x2 + 47x + -7 = 0 Reorder the terms: -7 + 47x + 24x2 = 0 Solving -7 + 47x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.2916666667 + 1.958333333x + x2 = 0 Move the constant term to the right: Add '0.2916666667' to each side of the equation. -0.2916666667 + 1.958333333x + 0.2916666667 + x2 = 0 + 0.2916666667 Reorder the terms: -0.2916666667 + 0.2916666667 + 1.958333333x + x2 = 0 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + 1.958333333x + x2 = 0 + 0.2916666667 1.958333333x + x2 = 0 + 0.2916666667 Combine like terms: 0 + 0.2916666667 = 0.2916666667 1.958333333x + x2 = 0.2916666667 The x term is 1.958333333x. Take half its coefficient (0.9791666665). Square it (0.9587673608) and add it to both sides. Add '0.9587673608' to each side of the equation. 1.958333333x + 0.9587673608 + x2 = 0.2916666667 + 0.9587673608 Reorder the terms: 0.9587673608 + 1.958333333x + x2 = 0.2916666667 + 0.9587673608 Combine like terms: 0.2916666667 + 0.9587673608 = 1.2504340275 0.9587673608 + 1.958333333x + x2 = 1.2504340275 Factor a perfect square on the left side: (x + 0.9791666665)(x + 0.9791666665) = 1.2504340275 Calculate the square root of the right side: 1.118228075 Break this problem into two subproblems by setting (x + 0.9791666665) equal to 1.118228075 and -1.118228075.Subproblem 1
x + 0.9791666665 = 1.118228075 Simplifying x + 0.9791666665 = 1.118228075 Reorder the terms: 0.9791666665 + x = 1.118228075 Solving 0.9791666665 + x = 1.118228075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9791666665' to each side of the equation. 0.9791666665 + -0.9791666665 + x = 1.118228075 + -0.9791666665 Combine like terms: 0.9791666665 + -0.9791666665 = 0.0000000000 0.0000000000 + x = 1.118228075 + -0.9791666665 x = 1.118228075 + -0.9791666665 Combine like terms: 1.118228075 + -0.9791666665 = 0.1390614085 x = 0.1390614085 Simplifying x = 0.1390614085Subproblem 2
x + 0.9791666665 = -1.118228075 Simplifying x + 0.9791666665 = -1.118228075 Reorder the terms: 0.9791666665 + x = -1.118228075 Solving 0.9791666665 + x = -1.118228075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9791666665' to each side of the equation. 0.9791666665 + -0.9791666665 + x = -1.118228075 + -0.9791666665 Combine like terms: 0.9791666665 + -0.9791666665 = 0.0000000000 0.0000000000 + x = -1.118228075 + -0.9791666665 x = -1.118228075 + -0.9791666665 Combine like terms: -1.118228075 + -0.9791666665 = -2.0973947415 x = -2.0973947415 Simplifying x = -2.0973947415Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1390614085, -2.0973947415}
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