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Simplifying 3x2 + 6x + 2 = 1202 Reorder the terms: 2 + 6x + 3x2 = 1202 Solving 2 + 6x + 3x2 = 1202 Solving for variable 'x'. Reorder the terms: 2 + -1202 + 6x + 3x2 = 1202 + -1202 Combine like terms: 2 + -1202 = -1200 -1200 + 6x + 3x2 = 1202 + -1202 Combine like terms: 1202 + -1202 = 0 -1200 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-400 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-400 + 2x + x2)' equal to zero and attempt to solve: Simplifying -400 + 2x + x2 = 0 Solving -400 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 2x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 2x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 2x + x2 = 0 + 400 2x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 2x + x2 = 400 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 400 + 1 Reorder the terms: 1 + 2x + x2 = 400 + 1 Combine like terms: 400 + 1 = 401 1 + 2x + x2 = 401 Factor a perfect square on the left side: (x + 1)(x + 1) = 401 Calculate the square root of the right side: 20.024984395 Break this problem into two subproblems by setting (x + 1) equal to 20.024984395 and -20.024984395.Subproblem 1
x + 1 = 20.024984395 Simplifying x + 1 = 20.024984395 Reorder the terms: 1 + x = 20.024984395 Solving 1 + x = 20.024984395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 20.024984395 + -1 Combine like terms: 1 + -1 = 0 0 + x = 20.024984395 + -1 x = 20.024984395 + -1 Combine like terms: 20.024984395 + -1 = 19.024984395 x = 19.024984395 Simplifying x = 19.024984395Subproblem 2
x + 1 = -20.024984395 Simplifying x + 1 = -20.024984395 Reorder the terms: 1 + x = -20.024984395 Solving 1 + x = -20.024984395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -20.024984395 + -1 Combine like terms: 1 + -1 = 0 0 + x = -20.024984395 + -1 x = -20.024984395 + -1 Combine like terms: -20.024984395 + -1 = -21.024984395 x = -21.024984395 Simplifying x = -21.024984395Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.024984395, -21.024984395}Solution
x = {19.024984395, -21.024984395}
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