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Simplifying 2x2 + 12x + -210 = 0 Reorder the terms: -210 + 12x + 2x2 = 0 Solving -210 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-105 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-105 + 6x + x2)' equal to zero and attempt to solve: Simplifying -105 + 6x + x2 = 0 Solving -105 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + 6x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 6x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 6x + x2 = 0 + 105 6x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 6x + x2 = 105 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 = 105 + 9 Reorder the terms: 9 + 6x + x2 = 105 + 9 Combine like terms: 105 + 9 = 114 9 + 6x + x2 = 114 Factor a perfect square on the left side: (x + 3)(x + 3) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + 3) equal to 10.677078252 and -10.677078252.Subproblem 1
x + 3 = 10.677078252 Simplifying x + 3 = 10.677078252 Reorder the terms: 3 + x = 10.677078252 Solving 3 + x = 10.677078252 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 = 10.677078252 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.677078252 + -3 x = 10.677078252 + -3 Combine like terms: 10.677078252 + -3 = 7.677078252 x = 7.677078252 Simplifying x = 7.677078252Subproblem 2
x + 3 = -10.677078252 Simplifying x + 3 = -10.677078252 Reorder the terms: 3 + x = -10.677078252 Solving 3 + x = -10.677078252 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 = -10.677078252 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.677078252 + -3 x = -10.677078252 + -3 Combine like terms: -10.677078252 + -3 = -13.677078252 x = -13.677078252 Simplifying x = -13.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.677078252, -13.677078252}Solution
x = {7.677078252, -13.677078252}
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