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Simplifying 20x2 + 400x + 48000 = 0 Reorder the terms: 48000 + 400x + 20x2 = 0 Solving 48000 + 400x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(2400 + 20x + x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(2400 + 20x + x2)' equal to zero and attempt to solve: Simplifying 2400 + 20x + x2 = 0 Solving 2400 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2400' to each side of the equation. 2400 + 20x + -2400 + x2 = 0 + -2400 Reorder the terms: 2400 + -2400 + 20x + x2 = 0 + -2400 Combine like terms: 2400 + -2400 = 0 0 + 20x + x2 = 0 + -2400 20x + x2 = 0 + -2400 Combine like terms: 0 + -2400 = -2400 20x + x2 = -2400 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -2400 + 100 Reorder the terms: 100 + 20x + x2 = -2400 + 100 Combine like terms: -2400 + 100 = -2300 100 + 20x + x2 = -2300 Factor a perfect square on the left side: (x + 10)(x + 10) = -2300 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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