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Simplifying 16x2 + 64x + -21 = 0 Reorder the terms: -21 + 64x + 16x2 = 0 Solving -21 + 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'. -1.3125 + 4x + x2 = 0 Move the constant term to the right: Add '1.3125' to each side of the equation. -1.3125 + 4x + 1.3125 + x2 = 0 + 1.3125 Reorder the terms: -1.3125 + 1.3125 + 4x + x2 = 0 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + 4x + x2 = 0 + 1.3125 4x + x2 = 0 + 1.3125 Combine like terms: 0 + 1.3125 = 1.3125 4x + x2 = 1.3125 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 = 1.3125 + 4 Reorder the terms: 4 + 4x + x2 = 1.3125 + 4 Combine like terms: 1.3125 + 4 = 5.3125 4 + 4x + x2 = 5.3125 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (x + 2) equal to 2.304886114 and -2.304886114.Subproblem 1
x + 2 = 2.304886114 Simplifying x + 2 = 2.304886114 Reorder the terms: 2 + x = 2.304886114 Solving 2 + x = 2.304886114 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 = 2.304886114 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.304886114 + -2 x = 2.304886114 + -2 Combine like terms: 2.304886114 + -2 = 0.304886114 x = 0.304886114 Simplifying x = 0.304886114Subproblem 2
x + 2 = -2.304886114 Simplifying x + 2 = -2.304886114 Reorder the terms: 2 + x = -2.304886114 Solving 2 + x = -2.304886114 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 = -2.304886114 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.304886114 + -2 x = -2.304886114 + -2 Combine like terms: -2.304886114 + -2 = -4.304886114 x = -4.304886114 Simplifying x = -4.304886114Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.304886114, -4.304886114}
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