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Simplifying 4x2 + 21x + 16 = 0 Reorder the terms: 16 + 21x + 4x2 = 0 Solving 16 + 21x + 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 + 5.25x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 5.25x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 5.25x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5.25x + x2 = 0 + -4 5.25x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 5.25x + x2 = -4 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = -4 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = -4 + 6.890625 Combine like terms: -4 + 6.890625 = 2.890625 6.890625 + 5.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + 2.625) equal to 1.700183814 and -1.700183814.Subproblem 1
x + 2.625 = 1.700183814 Simplifying x + 2.625 = 1.700183814 Reorder the terms: 2.625 + x = 1.700183814 Solving 2.625 + x = 1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 1.700183814 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 1.700183814 + -2.625 x = 1.700183814 + -2.625 Combine like terms: 1.700183814 + -2.625 = -0.924816186 x = -0.924816186 Simplifying x = -0.924816186Subproblem 2
x + 2.625 = -1.700183814 Simplifying x + 2.625 = -1.700183814 Reorder the terms: 2.625 + x = -1.700183814 Solving 2.625 + x = -1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -1.700183814 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -1.700183814 + -2.625 x = -1.700183814 + -2.625 Combine like terms: -1.700183814 + -2.625 = -4.325183814 x = -4.325183814 Simplifying x = -4.325183814Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.924816186, -4.325183814}
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