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Simplifying 0 = 200x + -2x2 + -4250 Reorder the terms: 0 = -4250 + 200x + -2x2 Solving 0 = -4250 + 200x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 4250 = 4250 4250 + -200x + 2x2 = -4250 + 200x + -2x2 + 4250 + -200x + 2x2 Reorder the terms: 4250 + -200x + 2x2 = -4250 + 4250 + 200x + -200x + -2x2 + 2x2 Combine like terms: -4250 + 4250 = 0 4250 + -200x + 2x2 = 0 + 200x + -200x + -2x2 + 2x2 4250 + -200x + 2x2 = 200x + -200x + -2x2 + 2x2 Combine like terms: 200x + -200x = 0 4250 + -200x + 2x2 = 0 + -2x2 + 2x2 4250 + -200x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 4250 + -200x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2125 + -100x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2125 + -100x + x2)' equal to zero and attempt to solve: Simplifying 2125 + -100x + x2 = 0 Solving 2125 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2125' to each side of the equation. 2125 + -100x + -2125 + x2 = 0 + -2125 Reorder the terms: 2125 + -2125 + -100x + x2 = 0 + -2125 Combine like terms: 2125 + -2125 = 0 0 + -100x + x2 = 0 + -2125 -100x + x2 = 0 + -2125 Combine like terms: 0 + -2125 = -2125 -100x + x2 = -2125 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -2125 + 2500 Reorder the terms: 2500 + -100x + x2 = -2125 + 2500 Combine like terms: -2125 + 2500 = 375 2500 + -100x + x2 = 375 Factor a perfect square on the left side: (x + -50)(x + -50) = 375 Calculate the square root of the right side: 19.364916731 Break this problem into two subproblems by setting (x + -50) equal to 19.364916731 and -19.364916731.Subproblem 1
x + -50 = 19.364916731 Simplifying x + -50 = 19.364916731 Reorder the terms: -50 + x = 19.364916731 Solving -50 + x = 19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 19.364916731 + 50 Combine like terms: -50 + 50 = 0 0 + x = 19.364916731 + 50 x = 19.364916731 + 50 Combine like terms: 19.364916731 + 50 = 69.364916731 x = 69.364916731 Simplifying x = 69.364916731Subproblem 2
x + -50 = -19.364916731 Simplifying x + -50 = -19.364916731 Reorder the terms: -50 + x = -19.364916731 Solving -50 + x = -19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -19.364916731 + 50 Combine like terms: -50 + 50 = 0 0 + x = -19.364916731 + 50 x = -19.364916731 + 50 Combine like terms: -19.364916731 + 50 = 30.635083269 x = 30.635083269 Simplifying x = 30.635083269Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.364916731, 30.635083269}Solution
x = {69.364916731, 30.635083269}
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