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Simplifying 16x2 + -800x + 4000 = 0 Reorder the terms: 4000 + -800x + 16x2 = 0 Solving 4000 + -800x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(250 + -50x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(250 + -50x + x2)' equal to zero and attempt to solve: Simplifying 250 + -50x + x2 = 0 Solving 250 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-250' to each side of the equation. 250 + -50x + -250 + x2 = 0 + -250 Reorder the terms: 250 + -250 + -50x + x2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -50x + x2 = 0 + -250 -50x + x2 = 0 + -250 Combine like terms: 0 + -250 = -250 -50x + x2 = -250 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -250 + 625 Reorder the terms: 625 + -50x + x2 = -250 + 625 Combine like terms: -250 + 625 = 375 625 + -50x + x2 = 375 Factor a perfect square on the left side: (x + -25)(x + -25) = 375 Calculate the square root of the right side: 19.364916731 Break this problem into two subproblems by setting (x + -25) equal to 19.364916731 and -19.364916731.Subproblem 1
x + -25 = 19.364916731 Simplifying x + -25 = 19.364916731 Reorder the terms: -25 + x = 19.364916731 Solving -25 + x = 19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 19.364916731 + 25 Combine like terms: -25 + 25 = 0 0 + x = 19.364916731 + 25 x = 19.364916731 + 25 Combine like terms: 19.364916731 + 25 = 44.364916731 x = 44.364916731 Simplifying x = 44.364916731Subproblem 2
x + -25 = -19.364916731 Simplifying x + -25 = -19.364916731 Reorder the terms: -25 + x = -19.364916731 Solving -25 + x = -19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -19.364916731 + 25 Combine like terms: -25 + 25 = 0 0 + x = -19.364916731 + 25 x = -19.364916731 + 25 Combine like terms: -19.364916731 + 25 = 5.635083269 x = 5.635083269 Simplifying x = 5.635083269Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.364916731, 5.635083269}Solution
x = {44.364916731, 5.635083269}
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