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Simplifying 3x2 + 30x = 12 Reorder the terms: 30x + 3x2 = 12 Solving 30x + 3x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 30x + 3x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 10x + x2)' equal to zero and attempt to solve: Simplifying -4 + 10x + x2 = 0 Solving -4 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 10x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 10x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 10x + x2 = 0 + 4 10x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 10x + x2 = 4 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 = 4 + 25 Reorder the terms: 25 + 10x + x2 = 4 + 25 Combine like terms: 4 + 25 = 29 25 + 10x + x2 = 29 Factor a perfect square on the left side: (x + 5)(x + 5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 5) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 5 = 5.385164807 Simplifying x + 5 = 5.385164807 Reorder the terms: 5 + x = 5.385164807 Solving 5 + x = 5.385164807 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 = 5.385164807 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.385164807 + -5 x = 5.385164807 + -5 Combine like terms: 5.385164807 + -5 = 0.385164807 x = 0.385164807 Simplifying x = 0.385164807Subproblem 2
x + 5 = -5.385164807 Simplifying x + 5 = -5.385164807 Reorder the terms: 5 + x = -5.385164807 Solving 5 + x = -5.385164807 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 = -5.385164807 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.385164807 + -5 x = -5.385164807 + -5 Combine like terms: -5.385164807 + -5 = -10.385164807 x = -10.385164807 Simplifying x = -10.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.385164807, -10.385164807}Solution
x = {0.385164807, -10.385164807}
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