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Simplifying 720x + -2x2 = 400x + 11720 Reorder the terms: 720x + -2x2 = 11720 + 400x Solving 720x + -2x2 = 11720 + 400x Solving for variable 'x'. Reorder the terms: -11720 + 720x + -400x + -2x2 = 11720 + 400x + -11720 + -400x Combine like terms: 720x + -400x = 320x -11720 + 320x + -2x2 = 11720 + 400x + -11720 + -400x Reorder the terms: -11720 + 320x + -2x2 = 11720 + -11720 + 400x + -400x Combine like terms: 11720 + -11720 = 0 -11720 + 320x + -2x2 = 0 + 400x + -400x -11720 + 320x + -2x2 = 400x + -400x Combine like terms: 400x + -400x = 0 -11720 + 320x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5860 + 160x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5860 + 160x + -1x2)' equal to zero and attempt to solve: Simplifying -5860 + 160x + -1x2 = 0 Solving -5860 + 160x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5860 + -160x + x2 = 0 Move the constant term to the right: Add '-5860' to each side of the equation. 5860 + -160x + -5860 + x2 = 0 + -5860 Reorder the terms: 5860 + -5860 + -160x + x2 = 0 + -5860 Combine like terms: 5860 + -5860 = 0 0 + -160x + x2 = 0 + -5860 -160x + x2 = 0 + -5860 Combine like terms: 0 + -5860 = -5860 -160x + x2 = -5860 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 = -5860 + 6400 Reorder the terms: 6400 + -160x + x2 = -5860 + 6400 Combine like terms: -5860 + 6400 = 540 6400 + -160x + x2 = 540 Factor a perfect square on the left side: (x + -80)(x + -80) = 540 Calculate the square root of the right side: 23.237900077 Break this problem into two subproblems by setting (x + -80) equal to 23.237900077 and -23.237900077.Subproblem 1
x + -80 = 23.237900077 Simplifying x + -80 = 23.237900077 Reorder the terms: -80 + x = 23.237900077 Solving -80 + x = 23.237900077 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 = 23.237900077 + 80 Combine like terms: -80 + 80 = 0 0 + x = 23.237900077 + 80 x = 23.237900077 + 80 Combine like terms: 23.237900077 + 80 = 103.237900077 x = 103.237900077 Simplifying x = 103.237900077Subproblem 2
x + -80 = -23.237900077 Simplifying x + -80 = -23.237900077 Reorder the terms: -80 + x = -23.237900077 Solving -80 + x = -23.237900077 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 = -23.237900077 + 80 Combine like terms: -80 + 80 = 0 0 + x = -23.237900077 + 80 x = -23.237900077 + 80 Combine like terms: -23.237900077 + 80 = 56.762099923 x = 56.762099923 Simplifying x = 56.762099923Solution
The solution to the problem is based on the solutions from the subproblems. x = {103.237900077, 56.762099923}Solution
x = {103.237900077, 56.762099923}
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