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Simplifying (3x + -3) * 2 + -1(2x + -7) = (3x + 5)(3x + 5) Reorder the terms: (-3 + 3x) * 2 + -1(2x + -7) = (3x + 5)(3x + 5) Reorder the terms for easier multiplication: 2(-3 + 3x) + -1(2x + -7) = (3x + 5)(3x + 5) (-3 * 2 + 3x * 2) + -1(2x + -7) = (3x + 5)(3x + 5) (-6 + 6x) + -1(2x + -7) = (3x + 5)(3x + 5) Reorder the terms: -6 + 6x + -1(-7 + 2x) = (3x + 5)(3x + 5) -6 + 6x + (-7 * -1 + 2x * -1) = (3x + 5)(3x + 5) -6 + 6x + (7 + -2x) = (3x + 5)(3x + 5) Reorder the terms: -6 + 7 + 6x + -2x = (3x + 5)(3x + 5) Combine like terms: -6 + 7 = 1 1 + 6x + -2x = (3x + 5)(3x + 5) Combine like terms: 6x + -2x = 4x 1 + 4x = (3x + 5)(3x + 5) Reorder the terms: 1 + 4x = (5 + 3x)(3x + 5) Reorder the terms: 1 + 4x = (5 + 3x)(5 + 3x) Multiply (5 + 3x) * (5 + 3x) 1 + 4x = (5(5 + 3x) + 3x * (5 + 3x)) 1 + 4x = ((5 * 5 + 3x * 5) + 3x * (5 + 3x)) 1 + 4x = ((25 + 15x) + 3x * (5 + 3x)) 1 + 4x = (25 + 15x + (5 * 3x + 3x * 3x)) 1 + 4x = (25 + 15x + (15x + 9x2)) Combine like terms: 15x + 15x = 30x 1 + 4x = (25 + 30x + 9x2) Solving 1 + 4x = 25 + 30x + 9x2 Solving for variable 'x'. Reorder the terms: 1 + -25 + 4x + -30x + -9x2 = 25 + 30x + 9x2 + -25 + -30x + -9x2 Combine like terms: 1 + -25 = -24 -24 + 4x + -30x + -9x2 = 25 + 30x + 9x2 + -25 + -30x + -9x2 Combine like terms: 4x + -30x = -26x -24 + -26x + -9x2 = 25 + 30x + 9x2 + -25 + -30x + -9x2 Reorder the terms: -24 + -26x + -9x2 = 25 + -25 + 30x + -30x + 9x2 + -9x2 Combine like terms: 25 + -25 = 0 -24 + -26x + -9x2 = 0 + 30x + -30x + 9x2 + -9x2 -24 + -26x + -9x2 = 30x + -30x + 9x2 + -9x2 Combine like terms: 30x + -30x = 0 -24 + -26x + -9x2 = 0 + 9x2 + -9x2 -24 + -26x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -24 + -26x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 26x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 26x + 9x2)' equal to zero and attempt to solve: Simplifying 24 + 26x + 9x2 = 0 Solving 24 + 26x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.666666667 + 2.888888889x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 2.888888889x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 2.888888889x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 2.888888889x + x2 = 0 + -2.666666667 2.888888889x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 2.888888889x + x2 = -2.666666667 The x term is 2.888888889x. Take half its coefficient (1.444444445). Square it (2.086419755) and add it to both sides. Add '2.086419755' to each side of the equation. 2.888888889x + 2.086419755 + x2 = -2.666666667 + 2.086419755 Reorder the terms: 2.086419755 + 2.888888889x + x2 = -2.666666667 + 2.086419755 Combine like terms: -2.666666667 + 2.086419755 = -0.580246912 2.086419755 + 2.888888889x + x2 = -0.580246912 Factor a perfect square on the left side: (x + 1.444444445)(x + 1.444444445) = -0.580246912 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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