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Simplifying 9x2 + -64x + -84 = 0 Reorder the terms: -84 + -64x + 9x2 = 0 Solving -84 + -64x + 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'. -9.333333333 + -7.111111111x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -7.111111111x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -7.111111111x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -7.111111111x + x2 = 0 + 9.333333333 -7.111111111x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -7.111111111x + x2 = 9.333333333 The x term is -7.111111111x. Take half its coefficient (-3.555555556). Square it (12.64197531) and add it to both sides. Add '12.64197531' to each side of the equation. -7.111111111x + 12.64197531 + x2 = 9.333333333 + 12.64197531 Reorder the terms: 12.64197531 + -7.111111111x + x2 = 9.333333333 + 12.64197531 Combine like terms: 9.333333333 + 12.64197531 = 21.975308643 12.64197531 + -7.111111111x + x2 = 21.975308643 Factor a perfect square on the left side: (x + -3.555555556)(x + -3.555555556) = 21.975308643 Calculate the square root of the right side: 4.687782913 Break this problem into two subproblems by setting (x + -3.555555556) equal to 4.687782913 and -4.687782913.Subproblem 1
x + -3.555555556 = 4.687782913 Simplifying x + -3.555555556 = 4.687782913 Reorder the terms: -3.555555556 + x = 4.687782913 Solving -3.555555556 + x = 4.687782913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + x = 4.687782913 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = 4.687782913 + 3.555555556 x = 4.687782913 + 3.555555556 Combine like terms: 4.687782913 + 3.555555556 = 8.243338469 x = 8.243338469 Simplifying x = 8.243338469Subproblem 2
x + -3.555555556 = -4.687782913 Simplifying x + -3.555555556 = -4.687782913 Reorder the terms: -3.555555556 + x = -4.687782913 Solving -3.555555556 + x = -4.687782913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + x = -4.687782913 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = -4.687782913 + 3.555555556 x = -4.687782913 + 3.555555556 Combine like terms: -4.687782913 + 3.555555556 = -1.132227357 x = -1.132227357 Simplifying x = -1.132227357Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.243338469, -1.132227357}
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