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Simplifying 0 = 60x2 + -17x + -20 Reorder the terms: 0 = -20 + -17x + 60x2 Solving 0 = -20 + -17x + 60x2 Solving for variable 'x'. Combine like terms: 0 + 20 = 20 20 + 17x + -60x2 = -20 + -17x + 60x2 + 20 + 17x + -60x2 Reorder the terms: 20 + 17x + -60x2 = -20 + 20 + -17x + 17x + 60x2 + -60x2 Combine like terms: -20 + 20 = 0 20 + 17x + -60x2 = 0 + -17x + 17x + 60x2 + -60x2 20 + 17x + -60x2 = -17x + 17x + 60x2 + -60x2 Combine like terms: -17x + 17x = 0 20 + 17x + -60x2 = 0 + 60x2 + -60x2 20 + 17x + -60x2 = 60x2 + -60x2 Combine like terms: 60x2 + -60x2 = 0 20 + 17x + -60x2 = 0 Begin completing the square. Divide all terms by -60 the coefficient of the squared term: Divide each side by '-60'. -0.3333333333 + -0.2833333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.2833333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.2833333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.2833333333x + x2 = 0 + 0.3333333333 -0.2833333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.2833333333x + x2 = 0.3333333333 The x term is -0.2833333333x. Take half its coefficient (-0.1416666667). Square it (0.02006944445) and add it to both sides. Add '0.02006944445' to each side of the equation. -0.2833333333x + 0.02006944445 + x2 = 0.3333333333 + 0.02006944445 Reorder the terms: 0.02006944445 + -0.2833333333x + x2 = 0.3333333333 + 0.02006944445 Combine like terms: 0.3333333333 + 0.02006944445 = 0.35340277775 0.02006944445 + -0.2833333333x + x2 = 0.35340277775 Factor a perfect square on the left side: (x + -0.1416666667)(x + -0.1416666667) = 0.35340277775 Calculate the square root of the right side: 0.594476894 Break this problem into two subproblems by setting (x + -0.1416666667) equal to 0.594476894 and -0.594476894.Subproblem 1
x + -0.1416666667 = 0.594476894 Simplifying x + -0.1416666667 = 0.594476894 Reorder the terms: -0.1416666667 + x = 0.594476894 Solving -0.1416666667 + x = 0.594476894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1416666667' to each side of the equation. -0.1416666667 + 0.1416666667 + x = 0.594476894 + 0.1416666667 Combine like terms: -0.1416666667 + 0.1416666667 = 0.0000000000 0.0000000000 + x = 0.594476894 + 0.1416666667 x = 0.594476894 + 0.1416666667 Combine like terms: 0.594476894 + 0.1416666667 = 0.7361435607 x = 0.7361435607 Simplifying x = 0.7361435607Subproblem 2
x + -0.1416666667 = -0.594476894 Simplifying x + -0.1416666667 = -0.594476894 Reorder the terms: -0.1416666667 + x = -0.594476894 Solving -0.1416666667 + x = -0.594476894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1416666667' to each side of the equation. -0.1416666667 + 0.1416666667 + x = -0.594476894 + 0.1416666667 Combine like terms: -0.1416666667 + 0.1416666667 = 0.0000000000 0.0000000000 + x = -0.594476894 + 0.1416666667 x = -0.594476894 + 0.1416666667 Combine like terms: -0.594476894 + 0.1416666667 = -0.4528102273 x = -0.4528102273 Simplifying x = -0.4528102273Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7361435607, -0.4528102273}
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