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Simplifying 16x2 + 64x + 59 = 0 Reorder the terms: 59 + 64x + 16x2 = 0 Solving 59 + 64x + 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'. 3.6875 + 4x + x2 = 0 Move the constant term to the right: Add '-3.6875' to each side of the equation. 3.6875 + 4x + -3.6875 + x2 = 0 + -3.6875 Reorder the terms: 3.6875 + -3.6875 + 4x + x2 = 0 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + 4x + x2 = 0 + -3.6875 4x + x2 = 0 + -3.6875 Combine like terms: 0 + -3.6875 = -3.6875 4x + x2 = -3.6875 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.6875 + 4 Reorder the terms: 4 + 4x + x2 = -3.6875 + 4 Combine like terms: -3.6875 + 4 = 0.3125 4 + 4x + x2 = 0.3125 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x + 2) equal to 0.559016994 and -0.559016994.Subproblem 1
x + 2 = 0.559016994 Simplifying x + 2 = 0.559016994 Reorder the terms: 2 + x = 0.559016994 Solving 2 + x = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.559016994 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.559016994 + -2 x = 0.559016994 + -2 Combine like terms: 0.559016994 + -2 = -1.440983006 x = -1.440983006 Simplifying x = -1.440983006Subproblem 2
x + 2 = -0.559016994 Simplifying x + 2 = -0.559016994 Reorder the terms: 2 + x = -0.559016994 Solving 2 + x = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.559016994 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.559016994 + -2 x = -0.559016994 + -2 Combine like terms: -0.559016994 + -2 = -2.559016994 x = -2.559016994 Simplifying x = -2.559016994Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.440983006, -2.559016994}
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