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Simplifying 6x2 + -12x + 18 = 3x2 + -15 Reorder the terms: 18 + -12x + 6x2 = 3x2 + -15 Reorder the terms: 18 + -12x + 6x2 = -15 + 3x2 Solving 18 + -12x + 6x2 = -15 + 3x2 Solving for variable 'x'. Reorder the terms: 18 + 15 + -12x + 6x2 + -3x2 = -15 + 3x2 + 15 + -3x2 Combine like terms: 18 + 15 = 33 33 + -12x + 6x2 + -3x2 = -15 + 3x2 + 15 + -3x2 Combine like terms: 6x2 + -3x2 = 3x2 33 + -12x + 3x2 = -15 + 3x2 + 15 + -3x2 Reorder the terms: 33 + -12x + 3x2 = -15 + 15 + 3x2 + -3x2 Combine like terms: -15 + 15 = 0 33 + -12x + 3x2 = 0 + 3x2 + -3x2 33 + -12x + 3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 33 + -12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(11 + -4x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + -4x + x2)' equal to zero and attempt to solve: Simplifying 11 + -4x + x2 = 0 Solving 11 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -4x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -4x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4x + x2 = 0 + -11 -4x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -4x + x2 = -11 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -11 + 4 Reorder the terms: 4 + -4x + x2 = -11 + 4 Combine like terms: -11 + 4 = -7 4 + -4x + x2 = -7 Factor a perfect square on the left side: (x + -2)(x + -2) = -7 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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