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Simplifying 24x2 + -23x + -10 = 0 Reorder the terms: -10 + -23x + 24x2 = 0 Solving -10 + -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'. -0.4166666667 + -0.9583333333x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.9583333333x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.9583333333x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.9583333333x + x2 = 0 + 0.4166666667 -0.9583333333x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.9583333333x + x2 = 0.4166666667 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 = 0.4166666667 + 0.2296006945 Reorder the terms: 0.2296006945 + -0.9583333333x + x2 = 0.4166666667 + 0.2296006945 Combine like terms: 0.4166666667 + 0.2296006945 = 0.6462673612 0.2296006945 + -0.9583333333x + x2 = 0.6462673612 Factor a perfect square on the left side: (x + -0.4791666667)(x + -0.4791666667) = 0.6462673612 Calculate the square root of the right side: 0.803907558 Break this problem into two subproblems by setting (x + -0.4791666667) equal to 0.803907558 and -0.803907558.Subproblem 1
x + -0.4791666667 = 0.803907558 Simplifying x + -0.4791666667 = 0.803907558 Reorder the terms: -0.4791666667 + x = 0.803907558 Solving -0.4791666667 + x = 0.803907558 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 = 0.803907558 + 0.4791666667 Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000 0.0000000000 + x = 0.803907558 + 0.4791666667 x = 0.803907558 + 0.4791666667 Combine like terms: 0.803907558 + 0.4791666667 = 1.2830742247 x = 1.2830742247 Simplifying x = 1.2830742247Subproblem 2
x + -0.4791666667 = -0.803907558 Simplifying x + -0.4791666667 = -0.803907558 Reorder the terms: -0.4791666667 + x = -0.803907558 Solving -0.4791666667 + x = -0.803907558 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 = -0.803907558 + 0.4791666667 Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000 0.0000000000 + x = -0.803907558 + 0.4791666667 x = -0.803907558 + 0.4791666667 Combine like terms: -0.803907558 + 0.4791666667 = -0.3247408913 x = -0.3247408913 Simplifying x = -0.3247408913Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2830742247, -0.3247408913}
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