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Simplifying 4x2 + 21x + 8 = 0 Reorder the terms: 8 + 21x + 4x2 = 0 Solving 8 + 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'. 2 + 5.25x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5.25x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 5.25x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5.25x + x2 = 0 + -2 5.25x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 5.25x + x2 = -2 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 = -2 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = -2 + 6.890625 Combine like terms: -2 + 6.890625 = 4.890625 6.890625 + 5.25x + x2 = 4.890625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (x + 2.625) equal to 2.211475752 and -2.211475752.Subproblem 1
x + 2.625 = 2.211475752 Simplifying x + 2.625 = 2.211475752 Reorder the terms: 2.625 + x = 2.211475752 Solving 2.625 + x = 2.211475752 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 = 2.211475752 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 2.211475752 + -2.625 x = 2.211475752 + -2.625 Combine like terms: 2.211475752 + -2.625 = -0.413524248 x = -0.413524248 Simplifying x = -0.413524248Subproblem 2
x + 2.625 = -2.211475752 Simplifying x + 2.625 = -2.211475752 Reorder the terms: 2.625 + x = -2.211475752 Solving 2.625 + x = -2.211475752 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 = -2.211475752 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -2.211475752 + -2.625 x = -2.211475752 + -2.625 Combine like terms: -2.211475752 + -2.625 = -4.836475752 x = -4.836475752 Simplifying x = -4.836475752Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.413524248, -4.836475752}
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