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Simplifying -3x2 + -24 = 7x Reorder the terms: -24 + -3x2 = 7x Solving -24 + -3x2 = 7x Solving for variable 'x'. Reorder the terms: -24 + -7x + -3x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -24 + -7x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 7x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 7x + 3x2)' equal to zero and attempt to solve: Simplifying 24 + 7x + 3x2 = 0 Solving 24 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 2.333333333x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 2.333333333x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 2.333333333x + x2 = 0 + -8 2.333333333x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 2.333333333x + x2 = -8 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = -8 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -8 + 1.361111112 Combine like terms: -8 + 1.361111112 = -6.638888888 1.361111112 + 2.333333333x + x2 = -6.638888888 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = -6.638888888 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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