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Simplifying -1x2 + -10x + -1000 + -18x = x2 Reorder the terms: -1000 + -10x + -18x + -1x2 = x2 Combine like terms: -10x + -18x = -28x -1000 + -28x + -1x2 = x2 Solving -1000 + -28x + -1x2 = x2 Solving for variable 'x'. Combine like terms: -1x2 + -1x2 = -2x2 -1000 + -28x + -2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1000 + -28x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(500 + 14x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(500 + 14x + x2)' equal to zero and attempt to solve: Simplifying 500 + 14x + x2 = 0 Solving 500 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + 14x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + 14x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + 14x + x2 = 0 + -500 14x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 14x + x2 = -500 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -500 + 49 Reorder the terms: 49 + 14x + x2 = -500 + 49 Combine like terms: -500 + 49 = -451 49 + 14x + x2 = -451 Factor a perfect square on the left side: (x + 7)(x + 7) = -451 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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