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Simplifying 9x2 + -9x + -19 = 0 Reorder the terms: -19 + -9x + 9x2 = 0 Solving -19 + -9x + 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'. -2.111111111 + -1x + x2 = 0 Move the constant term to the right: Add '2.111111111' to each side of the equation. -2.111111111 + -1x + 2.111111111 + x2 = 0 + 2.111111111 Reorder the terms: -2.111111111 + 2.111111111 + -1x + x2 = 0 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + -1x + x2 = 0 + 2.111111111 -1x + x2 = 0 + 2.111111111 Combine like terms: 0 + 2.111111111 = 2.111111111 -1x + x2 = 2.111111111 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.111111111 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.111111111 + 0.25 Combine like terms: 2.111111111 + 0.25 = 2.361111111 0.25 + -1x + x2 = 2.361111111 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.361111111 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (x + -0.5) equal to 1.536590743 and -1.536590743.Subproblem 1
x + -0.5 = 1.536590743 Simplifying x + -0.5 = 1.536590743 Reorder the terms: -0.5 + x = 1.536590743 Solving -0.5 + x = 1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.536590743 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.536590743 + 0.5 x = 1.536590743 + 0.5 Combine like terms: 1.536590743 + 0.5 = 2.036590743 x = 2.036590743 Simplifying x = 2.036590743Subproblem 2
x + -0.5 = -1.536590743 Simplifying x + -0.5 = -1.536590743 Reorder the terms: -0.5 + x = -1.536590743 Solving -0.5 + x = -1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.536590743 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.536590743 + 0.5 x = -1.536590743 + 0.5 Combine like terms: -1.536590743 + 0.5 = -1.036590743 x = -1.036590743 Simplifying x = -1.036590743Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.036590743, -1.036590743}
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