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Simplifying 0 = x2 + 40x + 7000 Reorder the terms: 0 = 7000 + 40x + x2 Solving 0 = 7000 + 40x + x2 Solving for variable 'x'. Combine like terms: 0 + -7000 = -7000 -7000 + -40x + -1x2 = 7000 + 40x + x2 + -7000 + -40x + -1x2 Reorder the terms: -7000 + -40x + -1x2 = 7000 + -7000 + 40x + -40x + x2 + -1x2 Combine like terms: 7000 + -7000 = 0 -7000 + -40x + -1x2 = 0 + 40x + -40x + x2 + -1x2 -7000 + -40x + -1x2 = 40x + -40x + x2 + -1x2 Combine like terms: 40x + -40x = 0 -7000 + -40x + -1x2 = 0 + x2 + -1x2 -7000 + -40x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7000 + -40x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7000 + 40x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7000 + 40x + x2)' equal to zero and attempt to solve: Simplifying 7000 + 40x + x2 = 0 Solving 7000 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7000' to each side of the equation. 7000 + 40x + -7000 + x2 = 0 + -7000 Reorder the terms: 7000 + -7000 + 40x + x2 = 0 + -7000 Combine like terms: 7000 + -7000 = 0 0 + 40x + x2 = 0 + -7000 40x + x2 = 0 + -7000 Combine like terms: 0 + -7000 = -7000 40x + x2 = -7000 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -7000 + 400 Reorder the terms: 400 + 40x + x2 = -7000 + 400 Combine like terms: -7000 + 400 = -6600 400 + 40x + x2 = -6600 Factor a perfect square on the left side: (x + 20)(x + 20) = -6600 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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