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Simplifying 16x2 + 57x + 49 = 0 Reorder the terms: 49 + 57x + 16x2 = 0 Solving 49 + 57x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.0625 + 3.5625x + x2 = 0 Move the constant term to the right: Add '-3.0625' to each side of the equation. 3.0625 + 3.5625x + -3.0625 + x2 = 0 + -3.0625 Reorder the terms: 3.0625 + -3.0625 + 3.5625x + x2 = 0 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 0.0000 + 3.5625x + x2 = 0 + -3.0625 3.5625x + x2 = 0 + -3.0625 Combine like terms: 0 + -3.0625 = -3.0625 3.5625x + x2 = -3.0625 The x term is 3.5625x. Take half its coefficient (1.78125). Square it (3.172851563) and add it to both sides. Add '3.172851563' to each side of the equation. 3.5625x + 3.172851563 + x2 = -3.0625 + 3.172851563 Reorder the terms: 3.172851563 + 3.5625x + x2 = -3.0625 + 3.172851563 Combine like terms: -3.0625 + 3.172851563 = 0.110351563 3.172851563 + 3.5625x + x2 = 0.110351563 Factor a perfect square on the left side: (x + 1.78125)(x + 1.78125) = 0.110351563 Calculate the square root of the right side: 0.332192057 Break this problem into two subproblems by setting (x + 1.78125) equal to 0.332192057 and -0.332192057.Subproblem 1
x + 1.78125 = 0.332192057 Simplifying x + 1.78125 = 0.332192057 Reorder the terms: 1.78125 + x = 0.332192057 Solving 1.78125 + x = 0.332192057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.78125' to each side of the equation. 1.78125 + -1.78125 + x = 0.332192057 + -1.78125 Combine like terms: 1.78125 + -1.78125 = 0.00000 0.00000 + x = 0.332192057 + -1.78125 x = 0.332192057 + -1.78125 Combine like terms: 0.332192057 + -1.78125 = -1.449057943 x = -1.449057943 Simplifying x = -1.449057943Subproblem 2
x + 1.78125 = -0.332192057 Simplifying x + 1.78125 = -0.332192057 Reorder the terms: 1.78125 + x = -0.332192057 Solving 1.78125 + x = -0.332192057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.78125' to each side of the equation. 1.78125 + -1.78125 + x = -0.332192057 + -1.78125 Combine like terms: 1.78125 + -1.78125 = 0.00000 0.00000 + x = -0.332192057 + -1.78125 x = -0.332192057 + -1.78125 Combine like terms: -0.332192057 + -1.78125 = -2.113442057 x = -2.113442057 Simplifying x = -2.113442057Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.449057943, -2.113442057}
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