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Simplifying (2x + -2)(2x + 6) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Reorder the terms: (-2 + 2x)(2x + 6) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Reorder the terms: (-2 + 2x)(6 + 2x) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Multiply (-2 + 2x) * (6 + 2x) (-2(6 + 2x) + 2x * (6 + 2x)) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 ((6 * -2 + 2x * -2) + 2x * (6 + 2x)) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 ((-12 + -4x) + 2x * (6 + 2x)) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 (-12 + -4x + (6 * 2x + 2x * 2x)) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 (-12 + -4x + (12x + 4x2)) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Combine like terms: -4x + 12x = 8x (-12 + 8x + 4x2) + -1(3x + -2) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Reorder the terms: -12 + 8x + 4x2 + -1(-2 + 3x) * 2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Reorder the terms for easier multiplication: -12 + 8x + 4x2 + -1 * 2(-2 + 3x) = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Multiply -1 * 2 -12 + 8x + 4x2 + -2(-2 + 3x) = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 -12 + 8x + 4x2 + (-2 * -2 + 3x * -2) = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 -12 + 8x + 4x2 + (4 + -6x) = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Reorder the terms: -12 + 4 + 8x + -6x + 4x2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Combine like terms: -12 + 4 = -8 -8 + 8x + -6x + 4x2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Combine like terms: 8x + -6x = 2x -8 + 2x + 4x2 = (2x + -5) * 2 + -1(2x + 7)(2x + -1) + -217 Reorder the terms: -8 + 2x + 4x2 = (-5 + 2x) * 2 + -1(2x + 7)(2x + -1) + -217 Reorder the terms for easier multiplication: -8 + 2x + 4x2 = 2(-5 + 2x) + -1(2x + 7)(2x + -1) + -217 -8 + 2x + 4x2 = (-5 * 2 + 2x * 2) + -1(2x + 7)(2x + -1) + -217 -8 + 2x + 4x2 = (-10 + 4x) + -1(2x + 7)(2x + -1) + -217 Reorder the terms: -8 + 2x + 4x2 = -10 + 4x + -1(7 + 2x)(2x + -1) + -217 Reorder the terms: -8 + 2x + 4x2 = -10 + 4x + -1(7 + 2x)(-1 + 2x) + -217 Multiply (7 + 2x) * (-1 + 2x) -8 + 2x + 4x2 = -10 + 4x + -1(7(-1 + 2x) + 2x * (-1 + 2x)) + -217 -8 + 2x + 4x2 = -10 + 4x + -1((-1 * 7 + 2x * 7) + 2x * (-1 + 2x)) + -217 -8 + 2x + 4x2 = -10 + 4x + -1((-7 + 14x) + 2x * (-1 + 2x)) + -217 -8 + 2x + 4x2 = -10 + 4x + -1(-7 + 14x + (-1 * 2x + 2x * 2x)) + -217 -8 + 2x + 4x2 = -10 + 4x + -1(-7 + 14x + (-2x + 4x2)) + -217 Combine like terms: 14x + -2x = 12x -8 + 2x + 4x2 = -10 + 4x + -1(-7 + 12x + 4x2) + -217 -8 + 2x + 4x2 = -10 + 4x + (-7 * -1 + 12x * -1 + 4x2 * -1) + -217 -8 + 2x + 4x2 = -10 + 4x + (7 + -12x + -4x2) + -217 Reorder the terms: -8 + 2x + 4x2 = -10 + 7 + -217 + 4x + -12x + -4x2 Combine like terms: -10 + 7 = -3 -8 + 2x + 4x2 = -3 + -217 + 4x + -12x + -4x2 Combine like terms: -3 + -217 = -220 -8 + 2x + 4x2 = -220 + 4x + -12x + -4x2 Combine like terms: 4x + -12x = -8x -8 + 2x + 4x2 = -220 + -8x + -4x2 Solving -8 + 2x + 4x2 = -220 + -8x + -4x2 Solving for variable 'x'. Reorder the terms: -8 + 220 + 2x + 8x + 4x2 + 4x2 = -220 + -8x + -4x2 + 220 + 8x + 4x2 Combine like terms: -8 + 220 = 212 212 + 2x + 8x + 4x2 + 4x2 = -220 + -8x + -4x2 + 220 + 8x + 4x2 Combine like terms: 2x + 8x = 10x 212 + 10x + 4x2 + 4x2 = -220 + -8x + -4x2 + 220 + 8x + 4x2 Combine like terms: 4x2 + 4x2 = 8x2 212 + 10x + 8x2 = -220 + -8x + -4x2 + 220 + 8x + 4x2 Reorder the terms: 212 + 10x + 8x2 = -220 + 220 + -8x + 8x + -4x2 + 4x2 Combine like terms: -220 + 220 = 0 212 + 10x + 8x2 = 0 + -8x + 8x + -4x2 + 4x2 212 + 10x + 8x2 = -8x + 8x + -4x2 + 4x2 Combine like terms: -8x + 8x = 0 212 + 10x + 8x2 = 0 + -4x2 + 4x2 212 + 10x + 8x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 212 + 10x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(106 + 5x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(106 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying 106 + 5x + 4x2 = 0 Solving 106 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 26.5 + 1.25x + x2 = 0 Move the constant term to the right: Add '-26.5' to each side of the equation. 26.5 + 1.25x + -26.5 + x2 = 0 + -26.5 Reorder the terms: 26.5 + -26.5 + 1.25x + x2 = 0 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + 1.25x + x2 = 0 + -26.5 1.25x + x2 = 0 + -26.5 Combine like terms: 0 + -26.5 = -26.5 1.25x + x2 = -26.5 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -26.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -26.5 + 0.390625 Combine like terms: -26.5 + 0.390625 = -26.109375 0.390625 + 1.25x + x2 = -26.109375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -26.109375 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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