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Simplifying 2(x2 + -200x + 20000) = 0 Reorder the terms: 2(20000 + -200x + x2) = 0 (20000 * 2 + -200x * 2 + x2 * 2) = 0 (40000 + -400x + 2x2) = 0 Solving 40000 + -400x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(20000 + -200x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20000 + -200x + x2)' equal to zero and attempt to solve: Simplifying 20000 + -200x + x2 = 0 Solving 20000 + -200x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20000' to each side of the equation. 20000 + -200x + -20000 + x2 = 0 + -20000 Reorder the terms: 20000 + -20000 + -200x + x2 = 0 + -20000 Combine like terms: 20000 + -20000 = 0 0 + -200x + x2 = 0 + -20000 -200x + x2 = 0 + -20000 Combine like terms: 0 + -20000 = -20000 -200x + x2 = -20000 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -20000 + 10000 Reorder the terms: 10000 + -200x + x2 = -20000 + 10000 Combine like terms: -20000 + 10000 = -10000 10000 + -200x + x2 = -10000 Factor a perfect square on the left side: (x + -100)(x + -100) = -10000 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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