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Simplifying 5x2 + 24x + 23 = 0 Reorder the terms: 23 + 24x + 5x2 = 0 Solving 23 + 24x + 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'. 4.6 + 4.8x + x2 = 0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + 4.8x + -4.6 + x2 = 0 + -4.6 Reorder the terms: 4.6 + -4.6 + 4.8x + x2 = 0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + 4.8x + x2 = 0 + -4.6 4.8x + x2 = 0 + -4.6 Combine like terms: 0 + -4.6 = -4.6 4.8x + x2 = -4.6 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = -4.6 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = -4.6 + 5.76 Combine like terms: -4.6 + 5.76 = 1.16 5.76 + 4.8x + x2 = 1.16 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (x + 2.4) equal to 1.077032961 and -1.077032961.Subproblem 1
x + 2.4 = 1.077032961 Simplifying x + 2.4 = 1.077032961 Reorder the terms: 2.4 + x = 1.077032961 Solving 2.4 + x = 1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 1.077032961 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 1.077032961 + -2.4 x = 1.077032961 + -2.4 Combine like terms: 1.077032961 + -2.4 = -1.322967039 x = -1.322967039 Simplifying x = -1.322967039Subproblem 2
x + 2.4 = -1.077032961 Simplifying x + 2.4 = -1.077032961 Reorder the terms: 2.4 + x = -1.077032961 Solving 2.4 + x = -1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -1.077032961 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -1.077032961 + -2.4 x = -1.077032961 + -2.4 Combine like terms: -1.077032961 + -2.4 = -3.477032961 x = -3.477032961 Simplifying x = -3.477032961Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.322967039, -3.477032961}
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