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Simplifying 3x2 + 24x + 75 = 0 Reorder the terms: 75 + 24x + 3x2 = 0 Solving 75 + 24x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + 8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(25 + 8x + x2)' equal to zero and attempt to solve: Simplifying 25 + 8x + x2 = 0 Solving 25 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 8x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 8x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 8x + x2 = 0 + -25 8x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 8x + x2 = -25 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -25 + 16 Reorder the terms: 16 + 8x + x2 = -25 + 16 Combine like terms: -25 + 16 = -9 16 + 8x + x2 = -9 Factor a perfect square on the left side: (x + 4)(x + 4) = -9 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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