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Simplifying -19x2 + -190x + -38000 = 0 Reorder the terms: -38000 + -190x + -19x2 = 0 Solving -38000 + -190x + -19x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-19'. -19(2000 + 10x + x2) = 0 Ignore the factor -19.Subproblem 1
Set the factor '(2000 + 10x + x2)' equal to zero and attempt to solve: Simplifying 2000 + 10x + x2 = 0 Solving 2000 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + 10x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + 10x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + 10x + x2 = 0 + -2000 10x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 10x + x2 = -2000 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 = -2000 + 25 Reorder the terms: 25 + 10x + x2 = -2000 + 25 Combine like terms: -2000 + 25 = -1975 25 + 10x + x2 = -1975 Factor a perfect square on the left side: (x + 5)(x + 5) = -1975 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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