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Simplifying 2(5x + -7) = 6x(5x + 9) + 28 Reorder the terms: 2(-7 + 5x) = 6x(5x + 9) + 28 (-7 * 2 + 5x * 2) = 6x(5x + 9) + 28 (-14 + 10x) = 6x(5x + 9) + 28 Reorder the terms: -14 + 10x = 6x(9 + 5x) + 28 -14 + 10x = (9 * 6x + 5x * 6x) + 28 -14 + 10x = (54x + 30x2) + 28 Reorder the terms: -14 + 10x = 28 + 54x + 30x2 Solving -14 + 10x = 28 + 54x + 30x2 Solving for variable 'x'. Reorder the terms: -14 + -28 + 10x + -54x + -30x2 = 28 + 54x + 30x2 + -28 + -54x + -30x2 Combine like terms: -14 + -28 = -42 -42 + 10x + -54x + -30x2 = 28 + 54x + 30x2 + -28 + -54x + -30x2 Combine like terms: 10x + -54x = -44x -42 + -44x + -30x2 = 28 + 54x + 30x2 + -28 + -54x + -30x2 Reorder the terms: -42 + -44x + -30x2 = 28 + -28 + 54x + -54x + 30x2 + -30x2 Combine like terms: 28 + -28 = 0 -42 + -44x + -30x2 = 0 + 54x + -54x + 30x2 + -30x2 -42 + -44x + -30x2 = 54x + -54x + 30x2 + -30x2 Combine like terms: 54x + -54x = 0 -42 + -44x + -30x2 = 0 + 30x2 + -30x2 -42 + -44x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -42 + -44x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(21 + 22x + 15x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(21 + 22x + 15x2)' equal to zero and attempt to solve: Simplifying 21 + 22x + 15x2 = 0 Solving 21 + 22x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.4 + 1.466666667x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 1.466666667x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 1.466666667x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 1.466666667x + x2 = 0 + -1.4 1.466666667x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 1.466666667x + x2 = -1.4 The x term is 1.466666667x. Take half its coefficient (0.7333333335). Square it (0.5377777780) and add it to both sides. Add '0.5377777780' to each side of the equation. 1.466666667x + 0.5377777780 + x2 = -1.4 + 0.5377777780 Reorder the terms: 0.5377777780 + 1.466666667x + x2 = -1.4 + 0.5377777780 Combine like terms: -1.4 + 0.5377777780 = -0.862222222 0.5377777780 + 1.466666667x + x2 = -0.862222222 Factor a perfect square on the left side: (x + 0.7333333335)(x + 0.7333333335) = -0.862222222 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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