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Simplifying 0 = 3x2 + 228x + -3900 Reorder the terms: 0 = -3900 + 228x + 3x2 Solving 0 = -3900 + 228x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 3900 = 3900 3900 + -228x + -3x2 = -3900 + 228x + 3x2 + 3900 + -228x + -3x2 Reorder the terms: 3900 + -228x + -3x2 = -3900 + 3900 + 228x + -228x + 3x2 + -3x2 Combine like terms: -3900 + 3900 = 0 3900 + -228x + -3x2 = 0 + 228x + -228x + 3x2 + -3x2 3900 + -228x + -3x2 = 228x + -228x + 3x2 + -3x2 Combine like terms: 228x + -228x = 0 3900 + -228x + -3x2 = 0 + 3x2 + -3x2 3900 + -228x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 3900 + -228x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1300 + -76x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1300 + -76x + -1x2)' equal to zero and attempt to solve: Simplifying 1300 + -76x + -1x2 = 0 Solving 1300 + -76x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1300 + 76x + x2 = 0 Move the constant term to the right: Add '1300' to each side of the equation. -1300 + 76x + 1300 + x2 = 0 + 1300 Reorder the terms: -1300 + 1300 + 76x + x2 = 0 + 1300 Combine like terms: -1300 + 1300 = 0 0 + 76x + x2 = 0 + 1300 76x + x2 = 0 + 1300 Combine like terms: 0 + 1300 = 1300 76x + x2 = 1300 The x term is 76x. Take half its coefficient (38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. 76x + 1444 + x2 = 1300 + 1444 Reorder the terms: 1444 + 76x + x2 = 1300 + 1444 Combine like terms: 1300 + 1444 = 2744 1444 + 76x + x2 = 2744 Factor a perfect square on the left side: (x + 38)(x + 38) = 2744 Calculate the square root of the right side: 52.383203415 Break this problem into two subproblems by setting (x + 38) equal to 52.383203415 and -52.383203415.Subproblem 1
x + 38 = 52.383203415 Simplifying x + 38 = 52.383203415 Reorder the terms: 38 + x = 52.383203415 Solving 38 + x = 52.383203415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = 52.383203415 + -38 Combine like terms: 38 + -38 = 0 0 + x = 52.383203415 + -38 x = 52.383203415 + -38 Combine like terms: 52.383203415 + -38 = 14.383203415 x = 14.383203415 Simplifying x = 14.383203415Subproblem 2
x + 38 = -52.383203415 Simplifying x + 38 = -52.383203415 Reorder the terms: 38 + x = -52.383203415 Solving 38 + x = -52.383203415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = -52.383203415 + -38 Combine like terms: 38 + -38 = 0 0 + x = -52.383203415 + -38 x = -52.383203415 + -38 Combine like terms: -52.383203415 + -38 = -90.383203415 x = -90.383203415 Simplifying x = -90.383203415Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.383203415, -90.383203415}Solution
x = {14.383203415, -90.383203415}
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