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Simplifying 3x2 + 22x + -16 = x Reorder the terms: -16 + 22x + 3x2 = x Solving -16 + 22x + 3x2 = x Solving for variable 'x'. Reorder the terms: -16 + 22x + -1x + 3x2 = x + -1x Combine like terms: 22x + -1x = 21x -16 + 21x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -16 + 21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + 7x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 7x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 7x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 7x + x2 = 0 + 5.333333333 7x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 7x + x2 = 5.333333333 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 5.333333333 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 5.333333333 + 12.25 Combine like terms: 5.333333333 + 12.25 = 17.583333333 12.25 + 7x + x2 = 17.583333333 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 17.583333333 Calculate the square root of the right side: 4.193248542 Break this problem into two subproblems by setting (x + 3.5) equal to 4.193248542 and -4.193248542.Subproblem 1
x + 3.5 = 4.193248542 Simplifying x + 3.5 = 4.193248542 Reorder the terms: 3.5 + x = 4.193248542 Solving 3.5 + x = 4.193248542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.193248542 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.193248542 + -3.5 x = 4.193248542 + -3.5 Combine like terms: 4.193248542 + -3.5 = 0.693248542 x = 0.693248542 Simplifying x = 0.693248542Subproblem 2
x + 3.5 = -4.193248542 Simplifying x + 3.5 = -4.193248542 Reorder the terms: 3.5 + x = -4.193248542 Solving 3.5 + x = -4.193248542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.193248542 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.193248542 + -3.5 x = -4.193248542 + -3.5 Combine like terms: -4.193248542 + -3.5 = -7.693248542 x = -7.693248542 Simplifying x = -7.693248542Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.693248542, -7.693248542}
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