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Simplifying 33x2 + -50x + -17 = 0 Reorder the terms: -17 + -50x + 33x2 = 0 Solving -17 + -50x + 33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. -0.5151515152 + -1.515151515x + x2 = 0 Move the constant term to the right: Add '0.5151515152' to each side of the equation. -0.5151515152 + -1.515151515x + 0.5151515152 + x2 = 0 + 0.5151515152 Reorder the terms: -0.5151515152 + 0.5151515152 + -1.515151515x + x2 = 0 + 0.5151515152 Combine like terms: -0.5151515152 + 0.5151515152 = 0.0000000000 0.0000000000 + -1.515151515x + x2 = 0 + 0.5151515152 -1.515151515x + x2 = 0 + 0.5151515152 Combine like terms: 0 + 0.5151515152 = 0.5151515152 -1.515151515x + x2 = 0.5151515152 The x term is -1.515151515x. Take half its coefficient (-0.7575757575). Square it (0.5739210284) and add it to both sides. Add '0.5739210284' to each side of the equation. -1.515151515x + 0.5739210284 + x2 = 0.5151515152 + 0.5739210284 Reorder the terms: 0.5739210284 + -1.515151515x + x2 = 0.5151515152 + 0.5739210284 Combine like terms: 0.5151515152 + 0.5739210284 = 1.0890725436 0.5739210284 + -1.515151515x + x2 = 1.0890725436 Factor a perfect square on the left side: (x + -0.7575757575)(x + -0.7575757575) = 1.0890725436 Calculate the square root of the right side: 1.043586385 Break this problem into two subproblems by setting (x + -0.7575757575) equal to 1.043586385 and -1.043586385.Subproblem 1
x + -0.7575757575 = 1.043586385 Simplifying x + -0.7575757575 = 1.043586385 Reorder the terms: -0.7575757575 + x = 1.043586385 Solving -0.7575757575 + x = 1.043586385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7575757575' to each side of the equation. -0.7575757575 + 0.7575757575 + x = 1.043586385 + 0.7575757575 Combine like terms: -0.7575757575 + 0.7575757575 = 0.0000000000 0.0000000000 + x = 1.043586385 + 0.7575757575 x = 1.043586385 + 0.7575757575 Combine like terms: 1.043586385 + 0.7575757575 = 1.8011621425 x = 1.8011621425 Simplifying x = 1.8011621425Subproblem 2
x + -0.7575757575 = -1.043586385 Simplifying x + -0.7575757575 = -1.043586385 Reorder the terms: -0.7575757575 + x = -1.043586385 Solving -0.7575757575 + x = -1.043586385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7575757575' to each side of the equation. -0.7575757575 + 0.7575757575 + x = -1.043586385 + 0.7575757575 Combine like terms: -0.7575757575 + 0.7575757575 = 0.0000000000 0.0000000000 + x = -1.043586385 + 0.7575757575 x = -1.043586385 + 0.7575757575 Combine like terms: -1.043586385 + 0.7575757575 = -0.2860106275 x = -0.2860106275 Simplifying x = -0.2860106275Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8011621425, -0.2860106275}
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