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Simplifying 600x + -3x2 = 600 + -6x Solving 600x + -3x2 = 600 + -6x Solving for variable 'x'. Reorder the terms: -600 + 600x + 6x + -3x2 = 600 + -6x + -600 + 6x Combine like terms: 600x + 6x = 606x -600 + 606x + -3x2 = 600 + -6x + -600 + 6x Reorder the terms: -600 + 606x + -3x2 = 600 + -600 + -6x + 6x Combine like terms: 600 + -600 = 0 -600 + 606x + -3x2 = 0 + -6x + 6x -600 + 606x + -3x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -600 + 606x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-200 + 202x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-200 + 202x + -1x2)' equal to zero and attempt to solve: Simplifying -200 + 202x + -1x2 = 0 Solving -200 + 202x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 200 + -202x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -202x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -202x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -202x + x2 = 0 + -200 -202x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -202x + x2 = -200 The x term is -202x. Take half its coefficient (-101). Square it (10201) and add it to both sides. Add '10201' to each side of the equation. -202x + 10201 + x2 = -200 + 10201 Reorder the terms: 10201 + -202x + x2 = -200 + 10201 Combine like terms: -200 + 10201 = 10001 10201 + -202x + x2 = 10001 Factor a perfect square on the left side: (x + -101)(x + -101) = 10001 Calculate the square root of the right side: 100.004999875 Break this problem into two subproblems by setting (x + -101) equal to 100.004999875 and -100.004999875.Subproblem 1
x + -101 = 100.004999875 Simplifying x + -101 = 100.004999875 Reorder the terms: -101 + x = 100.004999875 Solving -101 + x = 100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '101' to each side of the equation. -101 + 101 + x = 100.004999875 + 101 Combine like terms: -101 + 101 = 0 0 + x = 100.004999875 + 101 x = 100.004999875 + 101 Combine like terms: 100.004999875 + 101 = 201.004999875 x = 201.004999875 Simplifying x = 201.004999875Subproblem 2
x + -101 = -100.004999875 Simplifying x + -101 = -100.004999875 Reorder the terms: -101 + x = -100.004999875 Solving -101 + x = -100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '101' to each side of the equation. -101 + 101 + x = -100.004999875 + 101 Combine like terms: -101 + 101 = 0 0 + x = -100.004999875 + 101 x = -100.004999875 + 101 Combine like terms: -100.004999875 + 101 = 0.995000125 x = 0.995000125 Simplifying x = 0.995000125Solution
The solution to the problem is based on the solutions from the subproblems. x = {201.004999875, 0.995000125}Solution
x = {201.004999875, 0.995000125}
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