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Simplifying 24x2 + 23x + -24 = 0 Reorder the terms: -24 + 23x + 24x2 = 0 Solving -24 + 23x + 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'. -1 + 0.9583333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.9583333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.9583333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.9583333333x + x2 = 0 + 1 0.9583333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.9583333333x + x2 = 1 The x term is 0.9583333333x. Take half its coefficient (0.4791666667). Square it (0.2296006945) and add it to both sides. Add '0.2296006945' to each side of the equation. 0.9583333333x + 0.2296006945 + x2 = 1 + 0.2296006945 Reorder the terms: 0.2296006945 + 0.9583333333x + x2 = 1 + 0.2296006945 Combine like terms: 1 + 0.2296006945 = 1.2296006945 0.2296006945 + 0.9583333333x + x2 = 1.2296006945 Factor a perfect square on the left side: (x + 0.4791666667)(x + 0.4791666667) = 1.2296006945 Calculate the square root of the right side: 1.108873615 Break this problem into two subproblems by setting (x + 0.4791666667) equal to 1.108873615 and -1.108873615.Subproblem 1
x + 0.4791666667 = 1.108873615 Simplifying x + 0.4791666667 = 1.108873615 Reorder the terms: 0.4791666667 + x = 1.108873615 Solving 0.4791666667 + x = 1.108873615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4791666667' to each side of the equation. 0.4791666667 + -0.4791666667 + x = 1.108873615 + -0.4791666667 Combine like terms: 0.4791666667 + -0.4791666667 = 0.0000000000 0.0000000000 + x = 1.108873615 + -0.4791666667 x = 1.108873615 + -0.4791666667 Combine like terms: 1.108873615 + -0.4791666667 = 0.6297069483 x = 0.6297069483 Simplifying x = 0.6297069483Subproblem 2
x + 0.4791666667 = -1.108873615 Simplifying x + 0.4791666667 = -1.108873615 Reorder the terms: 0.4791666667 + x = -1.108873615 Solving 0.4791666667 + x = -1.108873615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4791666667' to each side of the equation. 0.4791666667 + -0.4791666667 + x = -1.108873615 + -0.4791666667 Combine like terms: 0.4791666667 + -0.4791666667 = 0.0000000000 0.0000000000 + x = -1.108873615 + -0.4791666667 x = -1.108873615 + -0.4791666667 Combine like terms: -1.108873615 + -0.4791666667 = -1.5880402817 x = -1.5880402817 Simplifying x = -1.5880402817Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6297069483, -1.5880402817}
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