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Simplifying 20 + -1(2x + 6) = 5(2 + -1x) * 2x Reorder the terms: 20 + -1(6 + 2x) = 5(2 + -1x) * 2x 20 + (6 * -1 + 2x * -1) = 5(2 + -1x) * 2x 20 + (-6 + -2x) = 5(2 + -1x) * 2x Combine like terms: 20 + -6 = 14 14 + -2x = 5(2 + -1x) * 2x Reorder the terms for easier multiplication: 14 + -2x = 5 * 2x(2 + -1x) Multiply 5 * 2 14 + -2x = 10x(2 + -1x) 14 + -2x = (2 * 10x + -1x * 10x) 14 + -2x = (20x + -10x2) Solving 14 + -2x = 20x + -10x2 Solving for variable 'x'. Combine like terms: -2x + -20x = -22x 14 + -22x + 10x2 = 20x + -10x2 + -20x + 10x2 Reorder the terms: 14 + -22x + 10x2 = 20x + -20x + -10x2 + 10x2 Combine like terms: 20x + -20x = 0 14 + -22x + 10x2 = 0 + -10x2 + 10x2 14 + -22x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 14 + -22x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -11x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -11x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + -11x + 5x2 = 0 Solving 7 + -11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -2.2x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -2.2x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -2.2x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -2.2x + x2 = 0 + -1.4 -2.2x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -2.2x + x2 = -1.4 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = -1.4 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -1.4 + 1.21 Combine like terms: -1.4 + 1.21 = -0.19 1.21 + -2.2x + x2 = -0.19 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = -0.19 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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