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Simplifying 18(2x + -1) = 3(x + 5) * 3x Reorder the terms: 18(-1 + 2x) = 3(x + 5) * 3x (-1 * 18 + 2x * 18) = 3(x + 5) * 3x (-18 + 36x) = 3(x + 5) * 3x Reorder the terms: -18 + 36x = 3(5 + x) * 3x Reorder the terms for easier multiplication: -18 + 36x = 3 * 3x(5 + x) Multiply 3 * 3 -18 + 36x = 9x(5 + x) -18 + 36x = (5 * 9x + x * 9x) -18 + 36x = (45x + 9x2) Solving -18 + 36x = 45x + 9x2 Solving for variable 'x'. Combine like terms: 36x + -45x = -9x -18 + -9x + -9x2 = 45x + 9x2 + -45x + -9x2 Reorder the terms: -18 + -9x + -9x2 = 45x + -45x + 9x2 + -9x2 Combine like terms: 45x + -45x = 0 -18 + -9x + -9x2 = 0 + 9x2 + -9x2 -18 + -9x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -18 + -9x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-9'. -9(2 + x + x2) = 0 Ignore the factor -9.Subproblem 1
Set the factor '(2 + x + x2)' equal to zero and attempt to solve: Simplifying 2 + x + x2 = 0 Solving 2 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x + x2 = 0 + -2 x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 x + x2 = -2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -2 + 0.25 Reorder the terms: 0.25 + x + x2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + x + x2 = -1.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.75 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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