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Simplifying 18x2 + 160x + 75 = 0 Reorder the terms: 75 + 160x + 18x2 = 0 Solving 75 + 160x + 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'. 4.166666667 + 8.888888889x + x2 = 0 Move the constant term to the right: Add '-4.166666667' to each side of the equation. 4.166666667 + 8.888888889x + -4.166666667 + x2 = 0 + -4.166666667 Reorder the terms: 4.166666667 + -4.166666667 + 8.888888889x + x2 = 0 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + 8.888888889x + x2 = 0 + -4.166666667 8.888888889x + x2 = 0 + -4.166666667 Combine like terms: 0 + -4.166666667 = -4.166666667 8.888888889x + x2 = -4.166666667 The x term is 8.888888889x. Take half its coefficient (4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. 8.888888889x + 19.75308642 + x2 = -4.166666667 + 19.75308642 Reorder the terms: 19.75308642 + 8.888888889x + x2 = -4.166666667 + 19.75308642 Combine like terms: -4.166666667 + 19.75308642 = 15.586419753 19.75308642 + 8.888888889x + x2 = 15.586419753 Factor a perfect square on the left side: (x + 4.444444445)(x + 4.444444445) = 15.586419753 Calculate the square root of the right side: 3.947964001 Break this problem into two subproblems by setting (x + 4.444444445) equal to 3.947964001 and -3.947964001.Subproblem 1
x + 4.444444445 = 3.947964001 Simplifying x + 4.444444445 = 3.947964001 Reorder the terms: 4.444444445 + x = 3.947964001 Solving 4.444444445 + x = 3.947964001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.444444445' to each side of the equation. 4.444444445 + -4.444444445 + x = 3.947964001 + -4.444444445 Combine like terms: 4.444444445 + -4.444444445 = 0.000000000 0.000000000 + x = 3.947964001 + -4.444444445 x = 3.947964001 + -4.444444445 Combine like terms: 3.947964001 + -4.444444445 = -0.496480444 x = -0.496480444 Simplifying x = -0.496480444Subproblem 2
x + 4.444444445 = -3.947964001 Simplifying x + 4.444444445 = -3.947964001 Reorder the terms: 4.444444445 + x = -3.947964001 Solving 4.444444445 + x = -3.947964001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.444444445' to each side of the equation. 4.444444445 + -4.444444445 + x = -3.947964001 + -4.444444445 Combine like terms: 4.444444445 + -4.444444445 = 0.000000000 0.000000000 + x = -3.947964001 + -4.444444445 x = -3.947964001 + -4.444444445 Combine like terms: -3.947964001 + -4.444444445 = -8.392408446 x = -8.392408446 Simplifying x = -8.392408446Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.496480444, -8.392408446}
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