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Simplifying 4x2 + -21x + 22 = 0 Reorder the terms: 22 + -21x + 4x2 = 0 Solving 22 + -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'. 5.5 + -5.25x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -5.25x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -5.25x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -5.25x + x2 = 0 + -5.5 -5.25x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -5.25x + x2 = -5.5 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 = -5.5 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -5.5 + 6.890625 Combine like terms: -5.5 + 6.890625 = 1.390625 6.890625 + -5.25x + x2 = 1.390625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + -2.625) equal to 1.179247642 and -1.179247642.Subproblem 1
x + -2.625 = 1.179247642 Simplifying x + -2.625 = 1.179247642 Reorder the terms: -2.625 + x = 1.179247642 Solving -2.625 + x = 1.179247642 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 = 1.179247642 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 1.179247642 + 2.625 x = 1.179247642 + 2.625 Combine like terms: 1.179247642 + 2.625 = 3.804247642 x = 3.804247642 Simplifying x = 3.804247642Subproblem 2
x + -2.625 = -1.179247642 Simplifying x + -2.625 = -1.179247642 Reorder the terms: -2.625 + x = -1.179247642 Solving -2.625 + x = -1.179247642 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 = -1.179247642 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -1.179247642 + 2.625 x = -1.179247642 + 2.625 Combine like terms: -1.179247642 + 2.625 = 1.445752358 x = 1.445752358 Simplifying x = 1.445752358Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.804247642, 1.445752358}
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