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Simplifying 3(2x + -5) = 5(x + 4) * x + 5 Reorder the terms: 3(-5 + 2x) = 5(x + 4) * x + 5 (-5 * 3 + 2x * 3) = 5(x + 4) * x + 5 (-15 + 6x) = 5(x + 4) * x + 5 Reorder the terms: -15 + 6x = 5(4 + x) * x + 5 Reorder the terms for easier multiplication: -15 + 6x = 5x(4 + x) + 5 -15 + 6x = (4 * 5x + x * 5x) + 5 -15 + 6x = (20x + 5x2) + 5 Reorder the terms: -15 + 6x = 5 + 20x + 5x2 Solving -15 + 6x = 5 + 20x + 5x2 Solving for variable 'x'. Reorder the terms: -15 + -5 + 6x + -20x + -5x2 = 5 + 20x + 5x2 + -5 + -20x + -5x2 Combine like terms: -15 + -5 = -20 -20 + 6x + -20x + -5x2 = 5 + 20x + 5x2 + -5 + -20x + -5x2 Combine like terms: 6x + -20x = -14x -20 + -14x + -5x2 = 5 + 20x + 5x2 + -5 + -20x + -5x2 Reorder the terms: -20 + -14x + -5x2 = 5 + -5 + 20x + -20x + 5x2 + -5x2 Combine like terms: 5 + -5 = 0 -20 + -14x + -5x2 = 0 + 20x + -20x + 5x2 + -5x2 -20 + -14x + -5x2 = 20x + -20x + 5x2 + -5x2 Combine like terms: 20x + -20x = 0 -20 + -14x + -5x2 = 0 + 5x2 + -5x2 -20 + -14x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -20 + -14x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 14x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 14x + 5x2)' equal to zero and attempt to solve: Simplifying 20 + 14x + 5x2 = 0 Solving 20 + 14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + 2.8x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2.8x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 2.8x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2.8x + x2 = 0 + -4 2.8x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 2.8x + x2 = -4 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = -4 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -4 + 1.96 Combine like terms: -4 + 1.96 = -2.04 1.96 + 2.8x + x2 = -2.04 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = -2.04 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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