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Simplifying 3x + 6x(200 + -1x) = 840 3x + (200 * 6x + -1x * 6x) = 840 3x + (1200x + -6x2) = 840 Combine like terms: 3x + 1200x = 1203x 1203x + -6x2 = 840 Solving 1203x + -6x2 = 840 Solving for variable 'x'. Reorder the terms: -840 + 1203x + -6x2 = 840 + -840 Combine like terms: 840 + -840 = 0 -840 + 1203x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-280 + 401x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-280 + 401x + -2x2)' equal to zero and attempt to solve: Simplifying -280 + 401x + -2x2 = 0 Solving -280 + 401x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 140 + -200.5x + x2 = 0 Move the constant term to the right: Add '-140' to each side of the equation. 140 + -200.5x + -140 + x2 = 0 + -140 Reorder the terms: 140 + -140 + -200.5x + x2 = 0 + -140 Combine like terms: 140 + -140 = 0 0 + -200.5x + x2 = 0 + -140 -200.5x + x2 = 0 + -140 Combine like terms: 0 + -140 = -140 -200.5x + x2 = -140 The x term is -200.5x. Take half its coefficient (-100.25). Square it (10050.0625) and add it to both sides. Add '10050.0625' to each side of the equation. -200.5x + 10050.0625 + x2 = -140 + 10050.0625 Reorder the terms: 10050.0625 + -200.5x + x2 = -140 + 10050.0625 Combine like terms: -140 + 10050.0625 = 9910.0625 10050.0625 + -200.5x + x2 = 9910.0625 Factor a perfect square on the left side: (x + -100.25)(x + -100.25) = 9910.0625 Calculate the square root of the right side: 99.549296833 Break this problem into two subproblems by setting (x + -100.25) equal to 99.549296833 and -99.549296833.Subproblem 1
x + -100.25 = 99.549296833 Simplifying x + -100.25 = 99.549296833 Reorder the terms: -100.25 + x = 99.549296833 Solving -100.25 + x = 99.549296833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100.25' to each side of the equation. -100.25 + 100.25 + x = 99.549296833 + 100.25 Combine like terms: -100.25 + 100.25 = 0.00 0.00 + x = 99.549296833 + 100.25 x = 99.549296833 + 100.25 Combine like terms: 99.549296833 + 100.25 = 199.799296833 x = 199.799296833 Simplifying x = 199.799296833Subproblem 2
x + -100.25 = -99.549296833 Simplifying x + -100.25 = -99.549296833 Reorder the terms: -100.25 + x = -99.549296833 Solving -100.25 + x = -99.549296833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100.25' to each side of the equation. -100.25 + 100.25 + x = -99.549296833 + 100.25 Combine like terms: -100.25 + 100.25 = 0.00 0.00 + x = -99.549296833 + 100.25 x = -99.549296833 + 100.25 Combine like terms: -99.549296833 + 100.25 = 0.700703167 x = 0.700703167 Simplifying x = 0.700703167Solution
The solution to the problem is based on the solutions from the subproblems. x = {199.799296833, 0.700703167}Solution
x = {199.799296833, 0.700703167}
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