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Simplifying -1(2x + -4) + -1(8x + -5) + 14 = -10x(x + -1) + -1(5x + 10) + 3 Reorder the terms: -1(-4 + 2x) + -1(8x + -5) + 14 = -10x(x + -1) + -1(5x + 10) + 3 (-4 * -1 + 2x * -1) + -1(8x + -5) + 14 = -10x(x + -1) + -1(5x + 10) + 3 (4 + -2x) + -1(8x + -5) + 14 = -10x(x + -1) + -1(5x + 10) + 3 Reorder the terms: 4 + -2x + -1(-5 + 8x) + 14 = -10x(x + -1) + -1(5x + 10) + 3 4 + -2x + (-5 * -1 + 8x * -1) + 14 = -10x(x + -1) + -1(5x + 10) + 3 4 + -2x + (5 + -8x) + 14 = -10x(x + -1) + -1(5x + 10) + 3 Reorder the terms: 4 + 5 + 14 + -2x + -8x = -10x(x + -1) + -1(5x + 10) + 3 Combine like terms: 4 + 5 = 9 9 + 14 + -2x + -8x = -10x(x + -1) + -1(5x + 10) + 3 Combine like terms: 9 + 14 = 23 23 + -2x + -8x = -10x(x + -1) + -1(5x + 10) + 3 Combine like terms: -2x + -8x = -10x 23 + -10x = -10x(x + -1) + -1(5x + 10) + 3 Reorder the terms: 23 + -10x = -10x(-1 + x) + -1(5x + 10) + 3 23 + -10x = (-1 * -10x + x * -10x) + -1(5x + 10) + 3 23 + -10x = (10x + -10x2) + -1(5x + 10) + 3 Reorder the terms: 23 + -10x = 10x + -10x2 + -1(10 + 5x) + 3 23 + -10x = 10x + -10x2 + (10 * -1 + 5x * -1) + 3 23 + -10x = 10x + -10x2 + (-10 + -5x) + 3 Reorder the terms: 23 + -10x = -10 + 3 + 10x + -5x + -10x2 Combine like terms: -10 + 3 = -7 23 + -10x = -7 + 10x + -5x + -10x2 Combine like terms: 10x + -5x = 5x 23 + -10x = -7 + 5x + -10x2 Solving 23 + -10x = -7 + 5x + -10x2 Solving for variable 'x'. Reorder the terms: 23 + 7 + -10x + -5x + 10x2 = -7 + 5x + -10x2 + 7 + -5x + 10x2 Combine like terms: 23 + 7 = 30 30 + -10x + -5x + 10x2 = -7 + 5x + -10x2 + 7 + -5x + 10x2 Combine like terms: -10x + -5x = -15x 30 + -15x + 10x2 = -7 + 5x + -10x2 + 7 + -5x + 10x2 Reorder the terms: 30 + -15x + 10x2 = -7 + 7 + 5x + -5x + -10x2 + 10x2 Combine like terms: -7 + 7 = 0 30 + -15x + 10x2 = 0 + 5x + -5x + -10x2 + 10x2 30 + -15x + 10x2 = 5x + -5x + -10x2 + 10x2 Combine like terms: 5x + -5x = 0 30 + -15x + 10x2 = 0 + -10x2 + 10x2 30 + -15x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 30 + -15x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(6 + -3x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + -3x + 2x2 = 0 Solving 6 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -1.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -1.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1.5x + x2 = 0 + -3 -1.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1.5x + x2 = -3 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -3 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -3 + 0.5625 Combine like terms: -3 + 0.5625 = -2.4375 0.5625 + -1.5x + x2 = -2.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -2.4375 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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