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Simplifying 4x2 + -21x + 12 = 0 Reorder the terms: 12 + -21x + 4x2 = 0 Solving 12 + -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'. 3 + -5.25x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5.25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -5.25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5.25x + x2 = 0 + -3 -5.25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5.25x + x2 = -3 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 = -3 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -3 + 6.890625 Combine like terms: -3 + 6.890625 = 3.890625 6.890625 + -5.25x + x2 = 3.890625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (x + -2.625) equal to 1.97246673 and -1.97246673.Subproblem 1
x + -2.625 = 1.97246673 Simplifying x + -2.625 = 1.97246673 Reorder the terms: -2.625 + x = 1.97246673 Solving -2.625 + x = 1.97246673 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 = 1.97246673 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 1.97246673 + 2.625 x = 1.97246673 + 2.625 Combine like terms: 1.97246673 + 2.625 = 4.59746673 x = 4.59746673 Simplifying x = 4.59746673Subproblem 2
x + -2.625 = -1.97246673 Simplifying x + -2.625 = -1.97246673 Reorder the terms: -2.625 + x = -1.97246673 Solving -2.625 + x = -1.97246673 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 = -1.97246673 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -1.97246673 + 2.625 x = -1.97246673 + 2.625 Combine like terms: -1.97246673 + 2.625 = 0.65253327 x = 0.65253327 Simplifying x = 0.65253327Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.59746673, 0.65253327}
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