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Simplifying 3x2 + 48x + -300 = 0 Reorder the terms: -300 + 48x + 3x2 = 0 Solving -300 + 48x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-100 + 16x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-100 + 16x + x2)' equal to zero and attempt to solve: Simplifying -100 + 16x + x2 = 0 Solving -100 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 16x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 16x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 16x + x2 = 0 + 100 16x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 16x + x2 = 100 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 100 + 64 Reorder the terms: 64 + 16x + x2 = 100 + 64 Combine like terms: 100 + 64 = 164 64 + 16x + x2 = 164 Factor a perfect square on the left side: (x + 8)(x + 8) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (x + 8) equal to 12.806248475 and -12.806248475.Subproblem 1
x + 8 = 12.806248475 Simplifying x + 8 = 12.806248475 Reorder the terms: 8 + x = 12.806248475 Solving 8 + x = 12.806248475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 12.806248475 + -8 Combine like terms: 8 + -8 = 0 0 + x = 12.806248475 + -8 x = 12.806248475 + -8 Combine like terms: 12.806248475 + -8 = 4.806248475 x = 4.806248475 Simplifying x = 4.806248475Subproblem 2
x + 8 = -12.806248475 Simplifying x + 8 = -12.806248475 Reorder the terms: 8 + x = -12.806248475 Solving 8 + x = -12.806248475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -12.806248475 + -8 Combine like terms: 8 + -8 = 0 0 + x = -12.806248475 + -8 x = -12.806248475 + -8 Combine like terms: -12.806248475 + -8 = -20.806248475 x = -20.806248475 Simplifying x = -20.806248475Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.806248475, -20.806248475}Solution
x = {4.806248475, -20.806248475}
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