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Simplifying 9x2 + 23x + -72 = 0 Reorder the terms: -72 + 23x + 9x2 = 0 Solving -72 + 23x + 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'. -8 + 2.555555556x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2.555555556x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 2.555555556x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2.555555556x + x2 = 0 + 8 2.555555556x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 2.555555556x + x2 = 8 The x term is 2.555555556x. Take half its coefficient (1.277777778). Square it (1.632716050) and add it to both sides. Add '1.632716050' to each side of the equation. 2.555555556x + 1.632716050 + x2 = 8 + 1.632716050 Reorder the terms: 1.632716050 + 2.555555556x + x2 = 8 + 1.632716050 Combine like terms: 8 + 1.632716050 = 9.63271605 1.632716050 + 2.555555556x + x2 = 9.63271605 Factor a perfect square on the left side: (x + 1.277777778)(x + 1.277777778) = 9.63271605 Calculate the square root of the right side: 3.103661716 Break this problem into two subproblems by setting (x + 1.277777778) equal to 3.103661716 and -3.103661716.Subproblem 1
x + 1.277777778 = 3.103661716 Simplifying x + 1.277777778 = 3.103661716 Reorder the terms: 1.277777778 + x = 3.103661716 Solving 1.277777778 + x = 3.103661716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = 3.103661716 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = 3.103661716 + -1.277777778 x = 3.103661716 + -1.277777778 Combine like terms: 3.103661716 + -1.277777778 = 1.825883938 x = 1.825883938 Simplifying x = 1.825883938Subproblem 2
x + 1.277777778 = -3.103661716 Simplifying x + 1.277777778 = -3.103661716 Reorder the terms: 1.277777778 + x = -3.103661716 Solving 1.277777778 + x = -3.103661716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = -3.103661716 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = -3.103661716 + -1.277777778 x = -3.103661716 + -1.277777778 Combine like terms: -3.103661716 + -1.277777778 = -4.381439494 x = -4.381439494 Simplifying x = -4.381439494Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.825883938, -4.381439494}
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