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Simplifying 9x2 + -1x + -21 = 0 Reorder the terms: -21 + -1x + 9x2 = 0 Solving -21 + -1x + 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'. -2.333333333 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -0.1111111111x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -0.1111111111x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -0.1111111111x + x2 = 0 + 2.333333333 -0.1111111111x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -0.1111111111x + x2 = 2.333333333 The x term is -0.1111111111x. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x + 0.003086419752 + x2 = 2.333333333 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 2.333333333 + 0.003086419752 Combine like terms: 2.333333333 + 0.003086419752 = 2.336419752752 0.003086419752 + -0.1111111111x + x2 = 2.336419752752 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 2.336419752752 Calculate the square root of the right side: 1.528535166 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 1.528535166 and -1.528535166.Subproblem 1
x + -0.05555555555 = 1.528535166 Simplifying x + -0.05555555555 = 1.528535166 Reorder the terms: -0.05555555555 + x = 1.528535166 Solving -0.05555555555 + x = 1.528535166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 1.528535166 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 1.528535166 + 0.05555555555 x = 1.528535166 + 0.05555555555 Combine like terms: 1.528535166 + 0.05555555555 = 1.58409072155 x = 1.58409072155 Simplifying x = 1.58409072155Subproblem 2
x + -0.05555555555 = -1.528535166 Simplifying x + -0.05555555555 = -1.528535166 Reorder the terms: -0.05555555555 + x = -1.528535166 Solving -0.05555555555 + x = -1.528535166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -1.528535166 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -1.528535166 + 0.05555555555 x = -1.528535166 + 0.05555555555 Combine like terms: -1.528535166 + 0.05555555555 = -1.47297961045 x = -1.47297961045 Simplifying x = -1.47297961045Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.58409072155, -1.47297961045}
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