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Simplifying 0 = x2 + 35x + 750 Reorder the terms: 0 = 750 + 35x + x2 Solving 0 = 750 + 35x + x2 Solving for variable 'x'. Combine like terms: 0 + -750 = -750 -750 + -35x + -1x2 = 750 + 35x + x2 + -750 + -35x + -1x2 Reorder the terms: -750 + -35x + -1x2 = 750 + -750 + 35x + -35x + x2 + -1x2 Combine like terms: 750 + -750 = 0 -750 + -35x + -1x2 = 0 + 35x + -35x + x2 + -1x2 -750 + -35x + -1x2 = 35x + -35x + x2 + -1x2 Combine like terms: 35x + -35x = 0 -750 + -35x + -1x2 = 0 + x2 + -1x2 -750 + -35x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -750 + -35x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(750 + 35x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(750 + 35x + x2)' equal to zero and attempt to solve: Simplifying 750 + 35x + x2 = 0 Solving 750 + 35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-750' to each side of the equation. 750 + 35x + -750 + x2 = 0 + -750 Reorder the terms: 750 + -750 + 35x + x2 = 0 + -750 Combine like terms: 750 + -750 = 0 0 + 35x + x2 = 0 + -750 35x + x2 = 0 + -750 Combine like terms: 0 + -750 = -750 35x + x2 = -750 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -750 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -750 + 306.25 Combine like terms: -750 + 306.25 = -443.75 306.25 + 35x + x2 = -443.75 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = -443.75 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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