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Simplifying 18x2 + -57x + -85 = 0 Reorder the terms: -85 + -57x + 18x2 = 0 Solving -85 + -57x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -4.722222222 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '4.722222222' to each side of the equation. -4.722222222 + -3.166666667x + 4.722222222 + x2 = 0 + 4.722222222 Reorder the terms: -4.722222222 + 4.722222222 + -3.166666667x + x2 = 0 + 4.722222222 Combine like terms: -4.722222222 + 4.722222222 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + 4.722222222 -3.166666667x + x2 = 0 + 4.722222222 Combine like terms: 0 + 4.722222222 = 4.722222222 -3.166666667x + x2 = 4.722222222 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = 4.722222222 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 4.722222222 + 2.506944447 Combine like terms: 4.722222222 + 2.506944447 = 7.229166669 2.506944447 + -3.166666667x + x2 = 7.229166669 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 7.229166669 Calculate the square root of the right side: 2.688710968 Break this problem into two subproblems by setting (x + -1.583333334) equal to 2.688710968 and -2.688710968.Subproblem 1
x + -1.583333334 = 2.688710968 Simplifying x + -1.583333334 = 2.688710968 Reorder the terms: -1.583333334 + x = 2.688710968 Solving -1.583333334 + x = 2.688710968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 2.688710968 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 2.688710968 + 1.583333334 x = 2.688710968 + 1.583333334 Combine like terms: 2.688710968 + 1.583333334 = 4.272044302 x = 4.272044302 Simplifying x = 4.272044302Subproblem 2
x + -1.583333334 = -2.688710968 Simplifying x + -1.583333334 = -2.688710968 Reorder the terms: -1.583333334 + x = -2.688710968 Solving -1.583333334 + x = -2.688710968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -2.688710968 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -2.688710968 + 1.583333334 x = -2.688710968 + 1.583333334 Combine like terms: -2.688710968 + 1.583333334 = -1.105377634 x = -1.105377634 Simplifying x = -1.105377634Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.272044302, -1.105377634}
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