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Simplifying 3(x2 + 10x + 75) = 0 Reorder the terms: 3(75 + 10x + x2) = 0 (75 * 3 + 10x * 3 + x2 * 3) = 0 (225 + 30x + 3x2) = 0 Solving 225 + 30x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(75 + 10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(75 + 10x + x2)' equal to zero and attempt to solve: Simplifying 75 + 10x + x2 = 0 Solving 75 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + 10x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + 10x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + 10x + x2 = 0 + -75 10x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 10x + x2 = -75 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 = -75 + 25 Reorder the terms: 25 + 10x + x2 = -75 + 25 Combine like terms: -75 + 25 = -50 25 + 10x + x2 = -50 Factor a perfect square on the left side: (x + 5)(x + 5) = -50 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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