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Simplifying 2x2 + -500x = 40000 Reorder the terms: -500x + 2x2 = 40000 Solving -500x + 2x2 = 40000 Solving for variable 'x'. Reorder the terms: -40000 + -500x + 2x2 = 40000 + -40000 Combine like terms: 40000 + -40000 = 0 -40000 + -500x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20000 + -250x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20000 + -250x + x2)' equal to zero and attempt to solve: Simplifying -20000 + -250x + x2 = 0 Solving -20000 + -250x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20000' to each side of the equation. -20000 + -250x + 20000 + x2 = 0 + 20000 Reorder the terms: -20000 + 20000 + -250x + x2 = 0 + 20000 Combine like terms: -20000 + 20000 = 0 0 + -250x + x2 = 0 + 20000 -250x + x2 = 0 + 20000 Combine like terms: 0 + 20000 = 20000 -250x + x2 = 20000 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = 20000 + 15625 Reorder the terms: 15625 + -250x + x2 = 20000 + 15625 Combine like terms: 20000 + 15625 = 35625 15625 + -250x + x2 = 35625 Factor a perfect square on the left side: (x + -125)(x + -125) = 35625 Calculate the square root of the right side: 188.745860882 Break this problem into two subproblems by setting (x + -125) equal to 188.745860882 and -188.745860882.Subproblem 1
x + -125 = 188.745860882 Simplifying x + -125 = 188.745860882 Reorder the terms: -125 + x = 188.745860882 Solving -125 + x = 188.745860882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 188.745860882 + 125 Combine like terms: -125 + 125 = 0 0 + x = 188.745860882 + 125 x = 188.745860882 + 125 Combine like terms: 188.745860882 + 125 = 313.745860882 x = 313.745860882 Simplifying x = 313.745860882Subproblem 2
x + -125 = -188.745860882 Simplifying x + -125 = -188.745860882 Reorder the terms: -125 + x = -188.745860882 Solving -125 + x = -188.745860882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -188.745860882 + 125 Combine like terms: -125 + 125 = 0 0 + x = -188.745860882 + 125 x = -188.745860882 + 125 Combine like terms: -188.745860882 + 125 = -63.745860882 x = -63.745860882 Simplifying x = -63.745860882Solution
The solution to the problem is based on the solutions from the subproblems. x = {313.745860882, -63.745860882}Solution
x = {313.745860882, -63.745860882}
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