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Simplifying 2(3 + x) * 5x = -24 Reorder the terms for easier multiplication: 2 * 5x(3 + x) = -24 Multiply 2 * 5 10x(3 + x) = -24 (3 * 10x + x * 10x) = -24 (30x + 10x2) = -24 Solving 30x + 10x2 = -24 Solving for variable 'x'. Reorder the terms: 24 + 30x + 10x2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 30x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 15x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 15x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + 15x + 5x2 = 0 Solving 12 + 15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 3x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 3x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 3x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 3x + x2 = 0 + -2.4 3x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 3x + x2 = -2.4 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -2.4 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -2.4 + 2.25 Combine like terms: -2.4 + 2.25 = -0.15 2.25 + 3x + x2 = -0.15 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -0.15 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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