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Simplifying 4x2 + 16x + 1 = 0 Reorder the terms: 1 + 16x + 4x2 = 0 Solving 1 + 16x + 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'. 0.25 + 4x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 4x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 4x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 4x + x2 = 0 + -0.25 4x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 4x + x2 = -0.25 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 = -0.25 + 4 Reorder the terms: 4 + 4x + x2 = -0.25 + 4 Combine like terms: -0.25 + 4 = 3.75 4 + 4x + x2 = 3.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 2) equal to 1.936491673 and -1.936491673.Subproblem 1
x + 2 = 1.936491673 Simplifying x + 2 = 1.936491673 Reorder the terms: 2 + x = 1.936491673 Solving 2 + x = 1.936491673 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 = 1.936491673 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.936491673 + -2 x = 1.936491673 + -2 Combine like terms: 1.936491673 + -2 = -0.063508327 x = -0.063508327 Simplifying x = -0.063508327Subproblem 2
x + 2 = -1.936491673 Simplifying x + 2 = -1.936491673 Reorder the terms: 2 + x = -1.936491673 Solving 2 + x = -1.936491673 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 = -1.936491673 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.936491673 + -2 x = -1.936491673 + -2 Combine like terms: -1.936491673 + -2 = -3.936491673 x = -3.936491673 Simplifying x = -3.936491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.063508327, -3.936491673}
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