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Simplifying 7x2 + -27x + -18 = 0 Reorder the terms: -18 + -27x + 7x2 = 0 Solving -18 + -27x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + -3.857142857x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -3.857142857x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -3.857142857x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -3.857142857x + x2 = 0 + 2.571428571 -3.857142857x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -3.857142857x + x2 = 2.571428571 The x term is -3.857142857x. Take half its coefficient (-1.928571429). Square it (3.719387757) and add it to both sides. Add '3.719387757' to each side of the equation. -3.857142857x + 3.719387757 + x2 = 2.571428571 + 3.719387757 Reorder the terms: 3.719387757 + -3.857142857x + x2 = 2.571428571 + 3.719387757 Combine like terms: 2.571428571 + 3.719387757 = 6.290816328 3.719387757 + -3.857142857x + x2 = 6.290816328 Factor a perfect square on the left side: (x + -1.928571429)(x + -1.928571429) = 6.290816328 Calculate the square root of the right side: 2.508149981 Break this problem into two subproblems by setting (x + -1.928571429) equal to 2.508149981 and -2.508149981.Subproblem 1
x + -1.928571429 = 2.508149981 Simplifying x + -1.928571429 = 2.508149981 Reorder the terms: -1.928571429 + x = 2.508149981 Solving -1.928571429 + x = 2.508149981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.928571429' to each side of the equation. -1.928571429 + 1.928571429 + x = 2.508149981 + 1.928571429 Combine like terms: -1.928571429 + 1.928571429 = 0.000000000 0.000000000 + x = 2.508149981 + 1.928571429 x = 2.508149981 + 1.928571429 Combine like terms: 2.508149981 + 1.928571429 = 4.43672141 x = 4.43672141 Simplifying x = 4.43672141Subproblem 2
x + -1.928571429 = -2.508149981 Simplifying x + -1.928571429 = -2.508149981 Reorder the terms: -1.928571429 + x = -2.508149981 Solving -1.928571429 + x = -2.508149981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.928571429' to each side of the equation. -1.928571429 + 1.928571429 + x = -2.508149981 + 1.928571429 Combine like terms: -1.928571429 + 1.928571429 = 0.000000000 0.000000000 + x = -2.508149981 + 1.928571429 x = -2.508149981 + 1.928571429 Combine like terms: -2.508149981 + 1.928571429 = -0.579578552 x = -0.579578552 Simplifying x = -0.579578552Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.43672141, -0.579578552}
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