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Simplifying 9x2 + -14x + -21 = 0 Reorder the terms: -21 + -14x + 9x2 = 0 Solving -21 + -14x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.333333333 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -1.555555556x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -1.555555556x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -1.555555556x + x2 = 0 + 2.333333333 -1.555555556x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -1.555555556x + x2 = 2.333333333 The x term is -1.555555556x. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556x + 0.6049382720 + x2 = 2.333333333 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = 2.333333333 + 0.6049382720 Combine like terms: 2.333333333 + 0.6049382720 = 2.938271605 0.6049382720 + -1.555555556x + x2 = 2.938271605 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 2.938271605 Calculate the square root of the right side: 1.714138736 Break this problem into two subproblems by setting (x + -0.777777778) equal to 1.714138736 and -1.714138736.Subproblem 1
x + -0.777777778 = 1.714138736 Simplifying x + -0.777777778 = 1.714138736 Reorder the terms: -0.777777778 + x = 1.714138736 Solving -0.777777778 + x = 1.714138736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = 1.714138736 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 1.714138736 + 0.777777778 x = 1.714138736 + 0.777777778 Combine like terms: 1.714138736 + 0.777777778 = 2.491916514 x = 2.491916514 Simplifying x = 2.491916514Subproblem 2
x + -0.777777778 = -1.714138736 Simplifying x + -0.777777778 = -1.714138736 Reorder the terms: -0.777777778 + x = -1.714138736 Solving -0.777777778 + x = -1.714138736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = -1.714138736 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -1.714138736 + 0.777777778 x = -1.714138736 + 0.777777778 Combine like terms: -1.714138736 + 0.777777778 = -0.936360958 x = -0.936360958 Simplifying x = -0.936360958Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.491916514, -0.936360958}
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