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Simplifying 2x2 + 10x + 150 = 0 Reorder the terms: 150 + 10x + 2x2 = 0 Solving 150 + 10x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(75 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + 5x + x2)' equal to zero and attempt to solve: Simplifying 75 + 5x + x2 = 0 Solving 75 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + 5x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + 5x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + 5x + x2 = 0 + -75 5x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 5x + x2 = -75 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -75 + 6.25 Combine like terms: -75 + 6.25 = -68.75 6.25 + 5x + x2 = -68.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -68.75 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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