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Simplifying x(x + 4) + x(x + 2) = 2x * 2x + 12 Reorder the terms: x(4 + x) + x(x + 2) = 2x * 2x + 12 (4 * x + x * x) + x(x + 2) = 2x * 2x + 12 (4x + x2) + x(x + 2) = 2x * 2x + 12 Reorder the terms: 4x + x2 + x(2 + x) = 2x * 2x + 12 4x + x2 + (2 * x + x * x) = 2x * 2x + 12 4x + x2 + (2x + x2) = 2x * 2x + 12 Reorder the terms: 4x + 2x + x2 + x2 = 2x * 2x + 12 Combine like terms: 4x + 2x = 6x 6x + x2 + x2 = 2x * 2x + 12 Combine like terms: x2 + x2 = 2x2 6x + 2x2 = 2x * 2x + 12 Reorder the terms for easier multiplication: 6x + 2x2 = 2 * 2x * x + 12 Multiply 2 * 2 6x + 2x2 = 4x * x + 12 Multiply x * x 6x + 2x2 = 4x2 + 12 Reorder the terms: 6x + 2x2 = 12 + 4x2 Solving 6x + 2x2 = 12 + 4x2 Solving for variable 'x'. Reorder the terms: -12 + 6x + 2x2 + -4x2 = 12 + 4x2 + -12 + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 -12 + 6x + -2x2 = 12 + 4x2 + -12 + -4x2 Reorder the terms: -12 + 6x + -2x2 = 12 + -12 + 4x2 + -4x2 Combine like terms: 12 + -12 = 0 -12 + 6x + -2x2 = 0 + 4x2 + -4x2 -12 + 6x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -12 + 6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -6 + 3x + -1x2 = 0 Solving -6 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -3x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -3x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -3x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -3x + x2 = 0 + -6 -3x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -3x + x2 = -6 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -6 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -6 + 2.25 Combine like terms: -6 + 2.25 = -3.75 2.25 + -3x + x2 = -3.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -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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