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Simplifying 4x2 + 12x + 9 = 425 Reorder the terms: 9 + 12x + 4x2 = 425 Solving 9 + 12x + 4x2 = 425 Solving for variable 'x'. Reorder the terms: 9 + -425 + 12x + 4x2 = 425 + -425 Combine like terms: 9 + -425 = -416 -416 + 12x + 4x2 = 425 + -425 Combine like terms: 425 + -425 = 0 -416 + 12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-104 + 3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-104 + 3x + x2)' equal to zero and attempt to solve: Simplifying -104 + 3x + x2 = 0 Solving -104 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + 3x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 3x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 3x + x2 = 0 + 104 3x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 3x + x2 = 104 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 104 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 104 + 2.25 Combine like terms: 104 + 2.25 = 106.25 2.25 + 3x + x2 = 106.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + 1.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + 1.5 = 10.307764064 Simplifying x + 1.5 = 10.307764064 Reorder the terms: 1.5 + x = 10.307764064 Solving 1.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.307764064 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.307764064 + -1.5 x = 10.307764064 + -1.5 Combine like terms: 10.307764064 + -1.5 = 8.807764064 x = 8.807764064 Simplifying x = 8.807764064Subproblem 2
x + 1.5 = -10.307764064 Simplifying x + 1.5 = -10.307764064 Reorder the terms: 1.5 + x = -10.307764064 Solving 1.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.307764064 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.307764064 + -1.5 x = -10.307764064 + -1.5 Combine like terms: -10.307764064 + -1.5 = -11.807764064 x = -11.807764064 Simplifying x = -11.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.807764064, -11.807764064}Solution
x = {8.807764064, -11.807764064}
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