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Simplifying -5(8 + 3x) = 2x(3x + 1) (8 * -5 + 3x * -5) = 2x(3x + 1) (-40 + -15x) = 2x(3x + 1) Reorder the terms: -40 + -15x = 2x(1 + 3x) -40 + -15x = (1 * 2x + 3x * 2x) -40 + -15x = (2x + 6x2) Solving -40 + -15x = 2x + 6x2 Solving for variable 'x'. Combine like terms: -15x + -2x = -17x -40 + -17x + -6x2 = 2x + 6x2 + -2x + -6x2 Reorder the terms: -40 + -17x + -6x2 = 2x + -2x + 6x2 + -6x2 Combine like terms: 2x + -2x = 0 -40 + -17x + -6x2 = 0 + 6x2 + -6x2 -40 + -17x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -40 + -17x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 17x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 17x + 6x2)' equal to zero and attempt to solve: Simplifying 40 + 17x + 6x2 = 0 Solving 40 + 17x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 6.666666667 + 2.833333333x + x2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + 2.833333333x + -6.666666667 + x2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + 2.833333333x + x2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + 2.833333333x + x2 = 0 + -6.666666667 2.833333333x + x2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 2.833333333x + x2 = -6.666666667 The x term is 2.833333333x. Take half its coefficient (1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. 2.833333333x + 2.006944445 + x2 = -6.666666667 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333x + x2 = -6.666666667 + 2.006944445 Combine like terms: -6.666666667 + 2.006944445 = -4.659722222 2.006944445 + 2.833333333x + x2 = -4.659722222 Factor a perfect square on the left side: (x + 1.416666667)(x + 1.416666667) = -4.659722222 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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