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Simplifying 7(10x + 2) + -1(5x + 2)(x + 12) = 10x + 2 Reorder the terms: 7(2 + 10x) + -1(5x + 2)(x + 12) = 10x + 2 (2 * 7 + 10x * 7) + -1(5x + 2)(x + 12) = 10x + 2 (14 + 70x) + -1(5x + 2)(x + 12) = 10x + 2 Reorder the terms: 14 + 70x + -1(2 + 5x)(x + 12) = 10x + 2 Reorder the terms: 14 + 70x + -1(2 + 5x)(12 + x) = 10x + 2 Multiply (2 + 5x) * (12 + x) 14 + 70x + -1(2(12 + x) + 5x * (12 + x)) = 10x + 2 14 + 70x + -1((12 * 2 + x * 2) + 5x * (12 + x)) = 10x + 2 14 + 70x + -1((24 + 2x) + 5x * (12 + x)) = 10x + 2 14 + 70x + -1(24 + 2x + (12 * 5x + x * 5x)) = 10x + 2 14 + 70x + -1(24 + 2x + (60x + 5x2)) = 10x + 2 Combine like terms: 2x + 60x = 62x 14 + 70x + -1(24 + 62x + 5x2) = 10x + 2 14 + 70x + (24 * -1 + 62x * -1 + 5x2 * -1) = 10x + 2 14 + 70x + (-24 + -62x + -5x2) = 10x + 2 Reorder the terms: 14 + -24 + 70x + -62x + -5x2 = 10x + 2 Combine like terms: 14 + -24 = -10 -10 + 70x + -62x + -5x2 = 10x + 2 Combine like terms: 70x + -62x = 8x -10 + 8x + -5x2 = 10x + 2 Reorder the terms: -10 + 8x + -5x2 = 2 + 10x Solving -10 + 8x + -5x2 = 2 + 10x Solving for variable 'x'. Reorder the terms: -10 + -2 + 8x + -10x + -5x2 = 2 + 10x + -2 + -10x Combine like terms: -10 + -2 = -12 -12 + 8x + -10x + -5x2 = 2 + 10x + -2 + -10x Combine like terms: 8x + -10x = -2x -12 + -2x + -5x2 = 2 + 10x + -2 + -10x Reorder the terms: -12 + -2x + -5x2 = 2 + -2 + 10x + -10x Combine like terms: 2 + -2 = 0 -12 + -2x + -5x2 = 0 + 10x + -10x -12 + -2x + -5x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -12 + -2x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 2x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + 2x + 5x2 = 0 Solving 12 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 0.4x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 0.4x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 0.4x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 0.4x + x2 = 0 + -2.4 0.4x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 0.4x + x2 = -2.4 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = -2.4 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = -2.4 + 0.04 Combine like terms: -2.4 + 0.04 = -2.36 0.04 + 0.4x + x2 = -2.36 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = -2.36 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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