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Simplifying 6x2 + 42x + 12 = 0 Reorder the terms: 12 + 42x + 6x2 = 0 Solving 12 + 42x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(2 + 7x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + 7x + x2)' equal to zero and attempt to solve: Simplifying 2 + 7x + x2 = 0 Solving 2 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 7x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 7x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7x + x2 = 0 + -2 7x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 7x + x2 = -2 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -2 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + 7x + x2 = 10.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 3.5 = 3.201562119 Simplifying x + 3.5 = 3.201562119 Reorder the terms: 3.5 + x = 3.201562119 Solving 3.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.201562119 + -3.5 x = 3.201562119 + -3.5 Combine like terms: 3.201562119 + -3.5 = -0.298437881 x = -0.298437881 Simplifying x = -0.298437881Subproblem 2
x + 3.5 = -3.201562119 Simplifying x + 3.5 = -3.201562119 Reorder the terms: 3.5 + x = -3.201562119 Solving 3.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.201562119 + -3.5 x = -3.201562119 + -3.5 Combine like terms: -3.201562119 + -3.5 = -6.701562119 x = -6.701562119 Simplifying x = -6.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.298437881, -6.701562119}Solution
x = {-0.298437881, -6.701562119}
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