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Simplifying 4x2 + -21x = 21 Reorder the terms: -21x + 4x2 = 21 Solving -21x + 4x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + -21x + 4x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + -5.25x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -5.25x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -5.25x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -5.25x + x2 = 0 + 5.25 -5.25x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -5.25x + x2 = 5.25 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 = 5.25 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = 5.25 + 6.890625 Combine like terms: 5.25 + 6.890625 = 12.140625 6.890625 + -5.25x + x2 = 12.140625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 12.140625 Calculate the square root of the right side: 3.484339966 Break this problem into two subproblems by setting (x + -2.625) equal to 3.484339966 and -3.484339966.Subproblem 1
x + -2.625 = 3.484339966 Simplifying x + -2.625 = 3.484339966 Reorder the terms: -2.625 + x = 3.484339966 Solving -2.625 + x = 3.484339966 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 = 3.484339966 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 3.484339966 + 2.625 x = 3.484339966 + 2.625 Combine like terms: 3.484339966 + 2.625 = 6.109339966 x = 6.109339966 Simplifying x = 6.109339966Subproblem 2
x + -2.625 = -3.484339966 Simplifying x + -2.625 = -3.484339966 Reorder the terms: -2.625 + x = -3.484339966 Solving -2.625 + x = -3.484339966 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 = -3.484339966 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -3.484339966 + 2.625 x = -3.484339966 + 2.625 Combine like terms: -3.484339966 + 2.625 = -0.859339966 x = -0.859339966 Simplifying x = -0.859339966Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.109339966, -0.859339966}
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