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Simplifying 18x2 + 360 * 17x + 360 = 0 Multiply 360 * 17 18x2 + 6120x + 360 = 0 Reorder the terms: 360 + 6120x + 18x2 = 0 Solving 360 + 6120x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '18'. 18(20 + 340x + x2) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(20 + 340x + x2)' equal to zero and attempt to solve: Simplifying 20 + 340x + x2 = 0 Solving 20 + 340x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 340x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 340x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 340x + x2 = 0 + -20 340x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 340x + x2 = -20 The x term is 340x. Take half its coefficient (170). Square it (28900) and add it to both sides. Add '28900' to each side of the equation. 340x + 28900 + x2 = -20 + 28900 Reorder the terms: 28900 + 340x + x2 = -20 + 28900 Combine like terms: -20 + 28900 = 28880 28900 + 340x + x2 = 28880 Factor a perfect square on the left side: (x + 170)(x + 170) = 28880 Calculate the square root of the right side: 169.94116629 Break this problem into two subproblems by setting (x + 170) equal to 169.94116629 and -169.94116629.Subproblem 1
x + 170 = 169.94116629 Simplifying x + 170 = 169.94116629 Reorder the terms: 170 + x = 169.94116629 Solving 170 + x = 169.94116629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-170' to each side of the equation. 170 + -170 + x = 169.94116629 + -170 Combine like terms: 170 + -170 = 0 0 + x = 169.94116629 + -170 x = 169.94116629 + -170 Combine like terms: 169.94116629 + -170 = -0.05883371 x = -0.05883371 Simplifying x = -0.05883371Subproblem 2
x + 170 = -169.94116629 Simplifying x + 170 = -169.94116629 Reorder the terms: 170 + x = -169.94116629 Solving 170 + x = -169.94116629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-170' to each side of the equation. 170 + -170 + x = -169.94116629 + -170 Combine like terms: 170 + -170 = 0 0 + x = -169.94116629 + -170 x = -169.94116629 + -170 Combine like terms: -169.94116629 + -170 = -339.94116629 x = -339.94116629 Simplifying x = -339.94116629Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.05883371, -339.94116629}Solution
x = {-0.05883371, -339.94116629}
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