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Simplifying 9x2 + -144x + 16 = 0 Reorder the terms: 16 + -144x + 9x2 = 0 Solving 16 + -144x + 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'. 1.777777778 + -16x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + -16x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + -16x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + -16x + x2 = 0 + -1.777777778 -16x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 -16x + x2 = -1.777777778 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -1.777777778 + 64 Reorder the terms: 64 + -16x + x2 = -1.777777778 + 64 Combine like terms: -1.777777778 + 64 = 62.222222222 64 + -16x + x2 = 62.222222222 Factor a perfect square on the left side: (x + -8)(x + -8) = 62.222222222 Calculate the square root of the right side: 7.888106377 Break this problem into two subproblems by setting (x + -8) equal to 7.888106377 and -7.888106377.Subproblem 1
x + -8 = 7.888106377 Simplifying x + -8 = 7.888106377 Reorder the terms: -8 + x = 7.888106377 Solving -8 + x = 7.888106377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.888106377 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.888106377 + 8 x = 7.888106377 + 8 Combine like terms: 7.888106377 + 8 = 15.888106377 x = 15.888106377 Simplifying x = 15.888106377Subproblem 2
x + -8 = -7.888106377 Simplifying x + -8 = -7.888106377 Reorder the terms: -8 + x = -7.888106377 Solving -8 + x = -7.888106377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.888106377 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.888106377 + 8 x = -7.888106377 + 8 Combine like terms: -7.888106377 + 8 = 0.111893623 x = 0.111893623 Simplifying x = 0.111893623Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.888106377, 0.111893623}
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