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Simplifying 5(x2 + 7x + 24) = 0 Reorder the terms: 5(24 + 7x + x2) = 0 (24 * 5 + 7x * 5 + x2 * 5) = 0 (120 + 35x + 5x2) = 0 Solving 120 + 35x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(24 + 7x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(24 + 7x + x2)' equal to zero and attempt to solve: Simplifying 24 + 7x + x2 = 0 Solving 24 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 7x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 7x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 7x + x2 = 0 + -24 7x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 7x + x2 = -24 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -24 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -24 + 12.25 Combine like terms: -24 + 12.25 = -11.75 12.25 + 7x + x2 = -11.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -11.75 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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