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Simplifying 81x2 + -330x + -7 = 0 Reorder the terms: -7 + -330x + 81x2 = 0 Solving -7 + -330x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.08641975309 + -4.074074074x + x2 = 0 Move the constant term to the right: Add '0.08641975309' to each side of the equation. -0.08641975309 + -4.074074074x + 0.08641975309 + x2 = 0 + 0.08641975309 Reorder the terms: -0.08641975309 + 0.08641975309 + -4.074074074x + x2 = 0 + 0.08641975309 Combine like terms: -0.08641975309 + 0.08641975309 = 0.00000000000 0.00000000000 + -4.074074074x + x2 = 0 + 0.08641975309 -4.074074074x + x2 = 0 + 0.08641975309 Combine like terms: 0 + 0.08641975309 = 0.08641975309 -4.074074074x + x2 = 0.08641975309 The x term is -4.074074074x. Take half its coefficient (-2.037037037). Square it (4.149519890) and add it to both sides. Add '4.149519890' to each side of the equation. -4.074074074x + 4.149519890 + x2 = 0.08641975309 + 4.149519890 Reorder the terms: 4.149519890 + -4.074074074x + x2 = 0.08641975309 + 4.149519890 Combine like terms: 0.08641975309 + 4.149519890 = 4.23593964309 4.149519890 + -4.074074074x + x2 = 4.23593964309 Factor a perfect square on the left side: (x + -2.037037037)(x + -2.037037037) = 4.23593964309 Calculate the square root of the right side: 2.05813985 Break this problem into two subproblems by setting (x + -2.037037037) equal to 2.05813985 and -2.05813985.Subproblem 1
x + -2.037037037 = 2.05813985 Simplifying x + -2.037037037 = 2.05813985 Reorder the terms: -2.037037037 + x = 2.05813985 Solving -2.037037037 + x = 2.05813985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.037037037' to each side of the equation. -2.037037037 + 2.037037037 + x = 2.05813985 + 2.037037037 Combine like terms: -2.037037037 + 2.037037037 = 0.000000000 0.000000000 + x = 2.05813985 + 2.037037037 x = 2.05813985 + 2.037037037 Combine like terms: 2.05813985 + 2.037037037 = 4.095176887 x = 4.095176887 Simplifying x = 4.095176887Subproblem 2
x + -2.037037037 = -2.05813985 Simplifying x + -2.037037037 = -2.05813985 Reorder the terms: -2.037037037 + x = -2.05813985 Solving -2.037037037 + x = -2.05813985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.037037037' to each side of the equation. -2.037037037 + 2.037037037 + x = -2.05813985 + 2.037037037 Combine like terms: -2.037037037 + 2.037037037 = 0.000000000 0.000000000 + x = -2.05813985 + 2.037037037 x = -2.05813985 + 2.037037037 Combine like terms: -2.05813985 + 2.037037037 = -0.021102813 x = -0.021102813 Simplifying x = -0.021102813Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.095176887, -0.021102813}
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