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Simplifying 5x2 + -23x + -24 = 0 Reorder the terms: -24 + -23x + 5x2 = 0 Solving -24 + -23x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + -4.6x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -4.6x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -4.6x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -4.6x + x2 = 0 + 4.8 -4.6x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -4.6x + x2 = 4.8 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 4.8 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 4.8 + 5.29 Combine like terms: 4.8 + 5.29 = 10.09 5.29 + -4.6x + x2 = 10.09 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 10.09 Calculate the square root of the right side: 3.176476035 Break this problem into two subproblems by setting (x + -2.3) equal to 3.176476035 and -3.176476035.Subproblem 1
x + -2.3 = 3.176476035 Simplifying x + -2.3 = 3.176476035 Reorder the terms: -2.3 + x = 3.176476035 Solving -2.3 + x = 3.176476035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 3.176476035 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 3.176476035 + 2.3 x = 3.176476035 + 2.3 Combine like terms: 3.176476035 + 2.3 = 5.476476035 x = 5.476476035 Simplifying x = 5.476476035Subproblem 2
x + -2.3 = -3.176476035 Simplifying x + -2.3 = -3.176476035 Reorder the terms: -2.3 + x = -3.176476035 Solving -2.3 + x = -3.176476035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -3.176476035 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -3.176476035 + 2.3 x = -3.176476035 + 2.3 Combine like terms: -3.176476035 + 2.3 = -0.876476035 x = -0.876476035 Simplifying x = -0.876476035Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.476476035, -0.876476035}
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