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Simplifying 24x2 + -3x + -1 = 0 Reorder the terms: -1 + -3x + 24x2 = 0 Solving -1 + -3x + 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'. -0.04166666667 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -0.125x + 0.04166666667 + x2 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -0.125x + x2 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -0.125x + x2 = 0 + 0.04166666667 -0.125x + x2 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -0.125x + x2 = 0.04166666667 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 0.04166666667 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.04166666667 + 0.00390625 Combine like terms: 0.04166666667 + 0.00390625 = 0.04557291667 0.00390625 + -0.125x + x2 = 0.04557291667 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.04557291667 Calculate the square root of the right side: 0.213478141 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.213478141 and -0.213478141.Subproblem 1
x + -0.0625 = 0.213478141 Simplifying x + -0.0625 = 0.213478141 Reorder the terms: -0.0625 + x = 0.213478141 Solving -0.0625 + x = 0.213478141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.213478141 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.213478141 + 0.0625 x = 0.213478141 + 0.0625 Combine like terms: 0.213478141 + 0.0625 = 0.275978141 x = 0.275978141 Simplifying x = 0.275978141Subproblem 2
x + -0.0625 = -0.213478141 Simplifying x + -0.0625 = -0.213478141 Reorder the terms: -0.0625 + x = -0.213478141 Solving -0.0625 + x = -0.213478141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.213478141 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.213478141 + 0.0625 x = -0.213478141 + 0.0625 Combine like terms: -0.213478141 + 0.0625 = -0.150978141 x = -0.150978141 Simplifying x = -0.150978141Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.275978141, -0.150978141}
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