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Simplifying 3x2 + 2x + -18 = 5x2 + 15 + -25 Reorder the terms: -18 + 2x + 3x2 = 5x2 + 15 + -25 Reorder the terms: -18 + 2x + 3x2 = 15 + -25 + 5x2 Combine like terms: 15 + -25 = -10 -18 + 2x + 3x2 = -10 + 5x2 Solving -18 + 2x + 3x2 = -10 + 5x2 Solving for variable 'x'. Reorder the terms: -18 + 10 + 2x + 3x2 + -5x2 = -10 + 5x2 + 10 + -5x2 Combine like terms: -18 + 10 = -8 -8 + 2x + 3x2 + -5x2 = -10 + 5x2 + 10 + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 -8 + 2x + -2x2 = -10 + 5x2 + 10 + -5x2 Reorder the terms: -8 + 2x + -2x2 = -10 + 10 + 5x2 + -5x2 Combine like terms: -10 + 10 = 0 -8 + 2x + -2x2 = 0 + 5x2 + -5x2 -8 + 2x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -8 + 2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + x + -1x2 = 0 Solving -4 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -1x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -1x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x + x2 = 0 + -4 -1x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1x + x2 = -4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -1x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 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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