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Simplifying 7x2 + -20x + -18 = 0 Reorder the terms: -18 + -20x + 7x2 = 0 Solving -18 + -20x + 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 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -2.857142857x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -2.857142857x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -2.857142857x + x2 = 0 + 2.571428571 -2.857142857x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -2.857142857x + x2 = 2.571428571 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 2.571428571 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 2.571428571 + 2.040816328 Combine like terms: 2.571428571 + 2.040816328 = 4.612244899 2.040816328 + -2.857142857x + x2 = 4.612244899 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 4.612244899 Calculate the square root of the right side: 2.147613769 Break this problem into two subproblems by setting (x + -1.428571429) equal to 2.147613769 and -2.147613769.Subproblem 1
x + -1.428571429 = 2.147613769 Simplifying x + -1.428571429 = 2.147613769 Reorder the terms: -1.428571429 + x = 2.147613769 Solving -1.428571429 + x = 2.147613769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 2.147613769 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 2.147613769 + 1.428571429 x = 2.147613769 + 1.428571429 Combine like terms: 2.147613769 + 1.428571429 = 3.576185198 x = 3.576185198 Simplifying x = 3.576185198Subproblem 2
x + -1.428571429 = -2.147613769 Simplifying x + -1.428571429 = -2.147613769 Reorder the terms: -1.428571429 + x = -2.147613769 Solving -1.428571429 + x = -2.147613769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -2.147613769 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -2.147613769 + 1.428571429 x = -2.147613769 + 1.428571429 Combine like terms: -2.147613769 + 1.428571429 = -0.71904234 x = -0.71904234 Simplifying x = -0.71904234Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.576185198, -0.71904234}
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