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Simplifying 16x2 + -219x + -35 = 0 Reorder the terms: -35 + -219x + 16x2 = 0 Solving -35 + -219x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.1875 + -13.6875x + x2 = 0 Move the constant term to the right: Add '2.1875' to each side of the equation. -2.1875 + -13.6875x + 2.1875 + x2 = 0 + 2.1875 Reorder the terms: -2.1875 + 2.1875 + -13.6875x + x2 = 0 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + -13.6875x + x2 = 0 + 2.1875 -13.6875x + x2 = 0 + 2.1875 Combine like terms: 0 + 2.1875 = 2.1875 -13.6875x + x2 = 2.1875 The x term is -13.6875x. Take half its coefficient (-6.84375). Square it (46.83691406) and add it to both sides. Add '46.83691406' to each side of the equation. -13.6875x + 46.83691406 + x2 = 2.1875 + 46.83691406 Reorder the terms: 46.83691406 + -13.6875x + x2 = 2.1875 + 46.83691406 Combine like terms: 2.1875 + 46.83691406 = 49.02441406 46.83691406 + -13.6875x + x2 = 49.02441406 Factor a perfect square on the left side: (x + -6.84375)(x + -6.84375) = 49.02441406 Calculate the square root of the right side: 7.001743644 Break this problem into two subproblems by setting (x + -6.84375) equal to 7.001743644 and -7.001743644.Subproblem 1
x + -6.84375 = 7.001743644 Simplifying x + -6.84375 = 7.001743644 Reorder the terms: -6.84375 + x = 7.001743644 Solving -6.84375 + x = 7.001743644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.84375' to each side of the equation. -6.84375 + 6.84375 + x = 7.001743644 + 6.84375 Combine like terms: -6.84375 + 6.84375 = 0.00000 0.00000 + x = 7.001743644 + 6.84375 x = 7.001743644 + 6.84375 Combine like terms: 7.001743644 + 6.84375 = 13.845493644 x = 13.845493644 Simplifying x = 13.845493644Subproblem 2
x + -6.84375 = -7.001743644 Simplifying x + -6.84375 = -7.001743644 Reorder the terms: -6.84375 + x = -7.001743644 Solving -6.84375 + x = -7.001743644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.84375' to each side of the equation. -6.84375 + 6.84375 + x = -7.001743644 + 6.84375 Combine like terms: -6.84375 + 6.84375 = 0.00000 0.00000 + x = -7.001743644 + 6.84375 x = -7.001743644 + 6.84375 Combine like terms: -7.001743644 + 6.84375 = -0.157993644 x = -0.157993644 Simplifying x = -0.157993644Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.845493644, -0.157993644}
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