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Simplifying 2.79x2 + -18.14x + -9.77 = 0 Reorder the terms: -9.77 + -18.14x + 2.79x2 = 0 Solving -9.77 + -18.14x + 2.79x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.79 the coefficient of the squared term: Divide each side by '2.79'. -3.501792115 + -6.501792115x + x2 = 0 Move the constant term to the right: Add '3.501792115' to each side of the equation. -3.501792115 + -6.501792115x + 3.501792115 + x2 = 0 + 3.501792115 Reorder the terms: -3.501792115 + 3.501792115 + -6.501792115x + x2 = 0 + 3.501792115 Combine like terms: -3.501792115 + 3.501792115 = 0.000000000 0.000000000 + -6.501792115x + x2 = 0 + 3.501792115 -6.501792115x + x2 = 0 + 3.501792115 Combine like terms: 0 + 3.501792115 = 3.501792115 -6.501792115x + x2 = 3.501792115 The x term is -6.501792115x. Take half its coefficient (-3.250896058). Square it (10.56832518) and add it to both sides. Add '10.56832518' to each side of the equation. -6.501792115x + 10.56832518 + x2 = 3.501792115 + 10.56832518 Reorder the terms: 10.56832518 + -6.501792115x + x2 = 3.501792115 + 10.56832518 Combine like terms: 3.501792115 + 10.56832518 = 14.070117295 10.56832518 + -6.501792115x + x2 = 14.070117295 Factor a perfect square on the left side: (x + -3.250896058)(x + -3.250896058) = 14.070117295 Calculate the square root of the right side: 3.751015502 Break this problem into two subproblems by setting (x + -3.250896058) equal to 3.751015502 and -3.751015502.Subproblem 1
x + -3.250896058 = 3.751015502 Simplifying x + -3.250896058 = 3.751015502 Reorder the terms: -3.250896058 + x = 3.751015502 Solving -3.250896058 + x = 3.751015502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.250896058' to each side of the equation. -3.250896058 + 3.250896058 + x = 3.751015502 + 3.250896058 Combine like terms: -3.250896058 + 3.250896058 = 0.000000000 0.000000000 + x = 3.751015502 + 3.250896058 x = 3.751015502 + 3.250896058 Combine like terms: 3.751015502 + 3.250896058 = 7.00191156 x = 7.00191156 Simplifying x = 7.00191156Subproblem 2
x + -3.250896058 = -3.751015502 Simplifying x + -3.250896058 = -3.751015502 Reorder the terms: -3.250896058 + x = -3.751015502 Solving -3.250896058 + x = -3.751015502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.250896058' to each side of the equation. -3.250896058 + 3.250896058 + x = -3.751015502 + 3.250896058 Combine like terms: -3.250896058 + 3.250896058 = 0.000000000 0.000000000 + x = -3.751015502 + 3.250896058 x = -3.751015502 + 3.250896058 Combine like terms: -3.751015502 + 3.250896058 = -0.500119444 x = -0.500119444 Simplifying x = -0.500119444Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.00191156, -0.500119444}
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