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Simplifying 3x + 7 = 9x2 + 25 Reorder the terms: 7 + 3x = 9x2 + 25 Reorder the terms: 7 + 3x = 25 + 9x2 Solving 7 + 3x = 25 + 9x2 Solving for variable 'x'. Reorder the terms: 7 + -25 + 3x + -9x2 = 25 + 9x2 + -25 + -9x2 Combine like terms: 7 + -25 = -18 -18 + 3x + -9x2 = 25 + 9x2 + -25 + -9x2 Reorder the terms: -18 + 3x + -9x2 = 25 + -25 + 9x2 + -9x2 Combine like terms: 25 + -25 = 0 -18 + 3x + -9x2 = 0 + 9x2 + -9x2 -18 + 3x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -18 + 3x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + x + -3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + x + -3x2)' equal to zero and attempt to solve: Simplifying -6 + x + -3x2 = 0 Solving -6 + x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.3333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -0.3333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.3333333333x + x2 = 0 + -2 -0.3333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.3333333333x + x2 = -2 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. -0.3333333333x + 0.25 + x2 = -2 + 0.25 Reorder the terms: 0.25 + -0.3333333333x + x2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + -0.3333333333x + x2 = -1.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.75 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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