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Simplifying 4x2 + -23x + -16 = 0 Reorder the terms: -16 + -23x + 4x2 = 0 Solving -16 + -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'. -4 + -5.75x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -5.75x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -5.75x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5.75x + x2 = 0 + 4 -5.75x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5.75x + x2 = 4 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 = 4 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 4 + 8.265625 Combine like terms: 4 + 8.265625 = 12.265625 8.265625 + -5.75x + x2 = 12.265625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 12.265625 Calculate the square root of the right side: 3.502231432 Break this problem into two subproblems by setting (x + -2.875) equal to 3.502231432 and -3.502231432.Subproblem 1
x + -2.875 = 3.502231432 Simplifying x + -2.875 = 3.502231432 Reorder the terms: -2.875 + x = 3.502231432 Solving -2.875 + x = 3.502231432 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 = 3.502231432 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.502231432 + 2.875 x = 3.502231432 + 2.875 Combine like terms: 3.502231432 + 2.875 = 6.377231432 x = 6.377231432 Simplifying x = 6.377231432Subproblem 2
x + -2.875 = -3.502231432 Simplifying x + -2.875 = -3.502231432 Reorder the terms: -2.875 + x = -3.502231432 Solving -2.875 + x = -3.502231432 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 = -3.502231432 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.502231432 + 2.875 x = -3.502231432 + 2.875 Combine like terms: -3.502231432 + 2.875 = -0.627231432 x = -0.627231432 Simplifying x = -0.627231432Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.377231432, -0.627231432}
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