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Simplifying 2(2x + 3) + -7x = 18 + 5x(x + 2x) Reorder the terms: 2(3 + 2x) + -7x = 18 + 5x(x + 2x) (3 * 2 + 2x * 2) + -7x = 18 + 5x(x + 2x) (6 + 4x) + -7x = 18 + 5x(x + 2x) Combine like terms: 4x + -7x = -3x 6 + -3x = 18 + 5x(x + 2x) Combine like terms: x + 2x = 3x 6 + -3x = 18 + 5x(3x) Remove parenthesis around (3x) 6 + -3x = 18 + 5x * 3x Reorder the terms for easier multiplication: 6 + -3x = 18 + 5 * 3x * x Multiply 5 * 3 6 + -3x = 18 + 15x * x Multiply x * x 6 + -3x = 18 + 15x2 Solving 6 + -3x = 18 + 15x2 Solving for variable 'x'. Reorder the terms: 6 + -18 + -3x + -15x2 = 18 + 15x2 + -18 + -15x2 Combine like terms: 6 + -18 = -12 -12 + -3x + -15x2 = 18 + 15x2 + -18 + -15x2 Reorder the terms: -12 + -3x + -15x2 = 18 + -18 + 15x2 + -15x2 Combine like terms: 18 + -18 = 0 -12 + -3x + -15x2 = 0 + 15x2 + -15x2 -12 + -3x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -12 + -3x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(4 + x + 5x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(4 + x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + x + 5x2 = 0 Solving 4 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 0.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 0.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 0.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 0.2x + x2 = 0 + -0.8 0.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 0.2x + x2 = -0.8 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. 0.2x + 0.25 + x2 = -0.8 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = -0.8 + 0.25 Combine like terms: -0.8 + 0.25 = -0.55 0.25 + 0.2x + x2 = -0.55 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.55 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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