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Simplifying 3x2 + 30x + -42 = 0 Reorder the terms: -42 + 30x + 3x2 = 0 Solving -42 + 30x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + 10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-14 + 10x + x2)' equal to zero and attempt to solve: Simplifying -14 + 10x + x2 = 0 Solving -14 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 10x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 10x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 10x + x2 = 0 + 14 10x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 10x + x2 = 14 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 14 + 25 Reorder the terms: 25 + 10x + x2 = 14 + 25 Combine like terms: 14 + 25 = 39 25 + 10x + x2 = 39 Factor a perfect square on the left side: (x + 5)(x + 5) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 5) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 5 = 6.244997998 Simplifying x + 5 = 6.244997998 Reorder the terms: 5 + x = 6.244997998 Solving 5 + x = 6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.244997998 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.244997998 + -5 x = 6.244997998 + -5 Combine like terms: 6.244997998 + -5 = 1.244997998 x = 1.244997998 Simplifying x = 1.244997998Subproblem 2
x + 5 = -6.244997998 Simplifying x + 5 = -6.244997998 Reorder the terms: 5 + x = -6.244997998 Solving 5 + x = -6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.244997998 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.244997998 + -5 x = -6.244997998 + -5 Combine like terms: -6.244997998 + -5 = -11.244997998 x = -11.244997998 Simplifying x = -11.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.244997998, -11.244997998}Solution
x = {1.244997998, -11.244997998}
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