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Simplifying 4x2 + 23x + 20 = 0 Reorder the terms: 20 + 23x + 4x2 = 0 Solving 20 + 23x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + 5.75x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5.75x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 5.75x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5.75x + x2 = 0 + -5 5.75x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 5.75x + x2 = -5 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = -5 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = -5 + 8.265625 Combine like terms: -5 + 8.265625 = 3.265625 8.265625 + 5.75x + x2 = 3.265625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + 2.875) equal to 1.807104037 and -1.807104037.Subproblem 1
x + 2.875 = 1.807104037 Simplifying x + 2.875 = 1.807104037 Reorder the terms: 2.875 + x = 1.807104037 Solving 2.875 + x = 1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 1.807104037 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 1.807104037 + -2.875 x = 1.807104037 + -2.875 Combine like terms: 1.807104037 + -2.875 = -1.067895963 x = -1.067895963 Simplifying x = -1.067895963Subproblem 2
x + 2.875 = -1.807104037 Simplifying x + 2.875 = -1.807104037 Reorder the terms: 2.875 + x = -1.807104037 Solving 2.875 + x = -1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -1.807104037 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -1.807104037 + -2.875 x = -1.807104037 + -2.875 Combine like terms: -1.807104037 + -2.875 = -4.682104037 x = -4.682104037 Simplifying x = -4.682104037Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.067895963, -4.682104037}
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