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Simplifying 2x(3x + -5) + 9 = 5 + -1(2x + 26) Reorder the terms: 2x(-5 + 3x) + 9 = 5 + -1(2x + 26) (-5 * 2x + 3x * 2x) + 9 = 5 + -1(2x + 26) (-10x + 6x2) + 9 = 5 + -1(2x + 26) Reorder the terms: 9 + -10x + 6x2 = 5 + -1(2x + 26) Reorder the terms: 9 + -10x + 6x2 = 5 + -1(26 + 2x) 9 + -10x + 6x2 = 5 + (26 * -1 + 2x * -1) 9 + -10x + 6x2 = 5 + (-26 + -2x) Combine like terms: 5 + -26 = -21 9 + -10x + 6x2 = -21 + -2x Solving 9 + -10x + 6x2 = -21 + -2x Solving for variable 'x'. Reorder the terms: 9 + 21 + -10x + 2x + 6x2 = -21 + -2x + 21 + 2x Combine like terms: 9 + 21 = 30 30 + -10x + 2x + 6x2 = -21 + -2x + 21 + 2x Combine like terms: -10x + 2x = -8x 30 + -8x + 6x2 = -21 + -2x + 21 + 2x Reorder the terms: 30 + -8x + 6x2 = -21 + 21 + -2x + 2x Combine like terms: -21 + 21 = 0 30 + -8x + 6x2 = 0 + -2x + 2x 30 + -8x + 6x2 = -2x + 2x Combine like terms: -2x + 2x = 0 30 + -8x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -4x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying 15 + -4x + 3x2 = 0 Solving 15 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -1.333333333x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -1.333333333x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1.333333333x + x2 = 0 + -5 -1.333333333x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1.333333333x + x2 = -5 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -5 + 0.4444444442 Combine like terms: -5 + 0.4444444442 = -4.5555555558 0.4444444442 + -1.333333333x + x2 = -4.5555555558 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -4.5555555558 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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