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Simplifying 36x2 + -12x + 21 = 22 Reorder the terms: 21 + -12x + 36x2 = 22 Solving 21 + -12x + 36x2 = 22 Solving for variable 'x'. Reorder the terms: 21 + -22 + -12x + 36x2 = 22 + -22 Combine like terms: 21 + -22 = -1 -1 + -12x + 36x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -1 + -12x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.02777777778 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.02777777778' to each side of the equation. -0.02777777778 + -0.3333333333x + 0.02777777778 + x2 = 0 + 0.02777777778 Reorder the terms: -0.02777777778 + 0.02777777778 + -0.3333333333x + x2 = 0 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + -0.3333333333x + x2 = 0 + 0.02777777778 -0.3333333333x + x2 = 0 + 0.02777777778 Combine like terms: 0 + 0.02777777778 = 0.02777777778 -0.3333333333x + x2 = 0.02777777778 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.02777777778 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.02777777778 + 0.02777777779 Combine like terms: 0.02777777778 + 0.02777777779 = 0.05555555557 0.02777777779 + -0.3333333333x + x2 = 0.05555555557 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.05555555557 Calculate the square root of the right side: 0.23570226 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.23570226 and -0.23570226.Subproblem 1
x + -0.1666666667 = 0.23570226 Simplifying x + -0.1666666667 = 0.23570226 Reorder the terms: -0.1666666667 + x = 0.23570226 Solving -0.1666666667 + x = 0.23570226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.23570226 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.23570226 + 0.1666666667 x = 0.23570226 + 0.1666666667 Combine like terms: 0.23570226 + 0.1666666667 = 0.4023689267 x = 0.4023689267 Simplifying x = 0.4023689267Subproblem 2
x + -0.1666666667 = -0.23570226 Simplifying x + -0.1666666667 = -0.23570226 Reorder the terms: -0.1666666667 + x = -0.23570226 Solving -0.1666666667 + x = -0.23570226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.23570226 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.23570226 + 0.1666666667 x = -0.23570226 + 0.1666666667 Combine like terms: -0.23570226 + 0.1666666667 = -0.0690355933 x = -0.0690355933 Simplifying x = -0.0690355933Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4023689267, -0.0690355933}
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