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Simplifying 33x2 + 15x + -17 = 0 Reorder the terms: -17 + 15x + 33x2 = 0 Solving -17 + 15x + 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 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '0.5151515152' to each side of the equation. -0.5151515152 + 0.4545454545x + 0.5151515152 + x2 = 0 + 0.5151515152 Reorder the terms: -0.5151515152 + 0.5151515152 + 0.4545454545x + x2 = 0 + 0.5151515152 Combine like terms: -0.5151515152 + 0.5151515152 = 0.0000000000 0.0000000000 + 0.4545454545x + x2 = 0 + 0.5151515152 0.4545454545x + x2 = 0 + 0.5151515152 Combine like terms: 0 + 0.5151515152 = 0.5151515152 0.4545454545x + x2 = 0.5151515152 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = 0.5151515152 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 0.5151515152 + 0.05165289257 Combine like terms: 0.5151515152 + 0.05165289257 = 0.56680440777 0.05165289257 + 0.4545454545x + x2 = 0.56680440777 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 0.56680440777 Calculate the square root of the right side: 0.752864136 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 0.752864136 and -0.752864136.Subproblem 1
x + 0.2272727273 = 0.752864136 Simplifying x + 0.2272727273 = 0.752864136 Reorder the terms: 0.2272727273 + x = 0.752864136 Solving 0.2272727273 + x = 0.752864136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = 0.752864136 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 0.752864136 + -0.2272727273 x = 0.752864136 + -0.2272727273 Combine like terms: 0.752864136 + -0.2272727273 = 0.5255914087 x = 0.5255914087 Simplifying x = 0.5255914087Subproblem 2
x + 0.2272727273 = -0.752864136 Simplifying x + 0.2272727273 = -0.752864136 Reorder the terms: 0.2272727273 + x = -0.752864136 Solving 0.2272727273 + x = -0.752864136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = -0.752864136 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -0.752864136 + -0.2272727273 x = -0.752864136 + -0.2272727273 Combine like terms: -0.752864136 + -0.2272727273 = -0.9801368633 x = -0.9801368633 Simplifying x = -0.9801368633Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5255914087, -0.9801368633}
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