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Simplifying 2(x2 + 6x + -414) = 0 Reorder the terms: 2(-414 + 6x + x2) = 0 (-414 * 2 + 6x * 2 + x2 * 2) = 0 (-828 + 12x + 2x2) = 0 Solving -828 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-414 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-414 + 6x + x2)' equal to zero and attempt to solve: Simplifying -414 + 6x + x2 = 0 Solving -414 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '414' to each side of the equation. -414 + 6x + 414 + x2 = 0 + 414 Reorder the terms: -414 + 414 + 6x + x2 = 0 + 414 Combine like terms: -414 + 414 = 0 0 + 6x + x2 = 0 + 414 6x + x2 = 0 + 414 Combine like terms: 0 + 414 = 414 6x + x2 = 414 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 414 + 9 Reorder the terms: 9 + 6x + x2 = 414 + 9 Combine like terms: 414 + 9 = 423 9 + 6x + x2 = 423 Factor a perfect square on the left side: (x + 3)(x + 3) = 423 Calculate the square root of the right side: 20.566963801 Break this problem into two subproblems by setting (x + 3) equal to 20.566963801 and -20.566963801.Subproblem 1
x + 3 = 20.566963801 Simplifying x + 3 = 20.566963801 Reorder the terms: 3 + x = 20.566963801 Solving 3 + x = 20.566963801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 20.566963801 + -3 Combine like terms: 3 + -3 = 0 0 + x = 20.566963801 + -3 x = 20.566963801 + -3 Combine like terms: 20.566963801 + -3 = 17.566963801 x = 17.566963801 Simplifying x = 17.566963801Subproblem 2
x + 3 = -20.566963801 Simplifying x + 3 = -20.566963801 Reorder the terms: 3 + x = -20.566963801 Solving 3 + x = -20.566963801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -20.566963801 + -3 Combine like terms: 3 + -3 = 0 0 + x = -20.566963801 + -3 x = -20.566963801 + -3 Combine like terms: -20.566963801 + -3 = -23.566963801 x = -23.566963801 Simplifying x = -23.566963801Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.566963801, -23.566963801}Solution
x = {17.566963801, -23.566963801}
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