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Simplifying 0 = 2x2 + -320x + 12050 Reorder the terms: 0 = 12050 + -320x + 2x2 Solving 0 = 12050 + -320x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -12050 = -12050 -12050 + 320x + -2x2 = 12050 + -320x + 2x2 + -12050 + 320x + -2x2 Reorder the terms: -12050 + 320x + -2x2 = 12050 + -12050 + -320x + 320x + 2x2 + -2x2 Combine like terms: 12050 + -12050 = 0 -12050 + 320x + -2x2 = 0 + -320x + 320x + 2x2 + -2x2 -12050 + 320x + -2x2 = -320x + 320x + 2x2 + -2x2 Combine like terms: -320x + 320x = 0 -12050 + 320x + -2x2 = 0 + 2x2 + -2x2 -12050 + 320x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12050 + 320x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6025 + 160x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6025 + 160x + -1x2)' equal to zero and attempt to solve: Simplifying -6025 + 160x + -1x2 = 0 Solving -6025 + 160x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6025 + -160x + x2 = 0 Move the constant term to the right: Add '-6025' to each side of the equation. 6025 + -160x + -6025 + x2 = 0 + -6025 Reorder the terms: 6025 + -6025 + -160x + x2 = 0 + -6025 Combine like terms: 6025 + -6025 = 0 0 + -160x + x2 = 0 + -6025 -160x + x2 = 0 + -6025 Combine like terms: 0 + -6025 = -6025 -160x + x2 = -6025 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = -6025 + 6400 Reorder the terms: 6400 + -160x + x2 = -6025 + 6400 Combine like terms: -6025 + 6400 = 375 6400 + -160x + x2 = 375 Factor a perfect square on the left side: (x + -80)(x + -80) = 375 Calculate the square root of the right side: 19.364916731 Break this problem into two subproblems by setting (x + -80) equal to 19.364916731 and -19.364916731.Subproblem 1
x + -80 = 19.364916731 Simplifying x + -80 = 19.364916731 Reorder the terms: -80 + x = 19.364916731 Solving -80 + x = 19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 19.364916731 + 80 Combine like terms: -80 + 80 = 0 0 + x = 19.364916731 + 80 x = 19.364916731 + 80 Combine like terms: 19.364916731 + 80 = 99.364916731 x = 99.364916731 Simplifying x = 99.364916731Subproblem 2
x + -80 = -19.364916731 Simplifying x + -80 = -19.364916731 Reorder the terms: -80 + x = -19.364916731 Solving -80 + x = -19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -19.364916731 + 80 Combine like terms: -80 + 80 = 0 0 + x = -19.364916731 + 80 x = -19.364916731 + 80 Combine like terms: -19.364916731 + 80 = 60.635083269 x = 60.635083269 Simplifying x = 60.635083269Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.364916731, 60.635083269}Solution
x = {99.364916731, 60.635083269}
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