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Simplifying 2c2 + -1000c + 800 = 0 Reorder the terms: 800 + -1000c + 2c2 = 0 Solving 800 + -1000c + 2c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(400 + -500c + c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(400 + -500c + c2)' equal to zero and attempt to solve: Simplifying 400 + -500c + c2 = 0 Solving 400 + -500c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-400' to each side of the equation. 400 + -500c + -400 + c2 = 0 + -400 Reorder the terms: 400 + -400 + -500c + c2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -500c + c2 = 0 + -400 -500c + c2 = 0 + -400 Combine like terms: 0 + -400 = -400 -500c + c2 = -400 The c term is -500c. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500c + 62500 + c2 = -400 + 62500 Reorder the terms: 62500 + -500c + c2 = -400 + 62500 Combine like terms: -400 + 62500 = 62100 62500 + -500c + c2 = 62100 Factor a perfect square on the left side: (c + -250)(c + -250) = 62100 Calculate the square root of the right side: 249.198715888 Break this problem into two subproblems by setting (c + -250) equal to 249.198715888 and -249.198715888.Subproblem 1
c + -250 = 249.198715888 Simplifying c + -250 = 249.198715888 Reorder the terms: -250 + c = 249.198715888 Solving -250 + c = 249.198715888 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + c = 249.198715888 + 250 Combine like terms: -250 + 250 = 0 0 + c = 249.198715888 + 250 c = 249.198715888 + 250 Combine like terms: 249.198715888 + 250 = 499.198715888 c = 499.198715888 Simplifying c = 499.198715888Subproblem 2
c + -250 = -249.198715888 Simplifying c + -250 = -249.198715888 Reorder the terms: -250 + c = -249.198715888 Solving -250 + c = -249.198715888 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + c = -249.198715888 + 250 Combine like terms: -250 + 250 = 0 0 + c = -249.198715888 + 250 c = -249.198715888 + 250 Combine like terms: -249.198715888 + 250 = 0.801284112 c = 0.801284112 Simplifying c = 0.801284112Solution
The solution to the problem is based on the solutions from the subproblems. c = {499.198715888, 0.801284112}Solution
c = {499.198715888, 0.801284112}
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