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Simplifying -2x(x + -3) + 7(2x + -4) + -6(x + 6) = 0 Reorder the terms: -2x(-3 + x) + 7(2x + -4) + -6(x + 6) = 0 (-3 * -2x + x * -2x) + 7(2x + -4) + -6(x + 6) = 0 (6x + -2x2) + 7(2x + -4) + -6(x + 6) = 0 Reorder the terms: 6x + -2x2 + 7(-4 + 2x) + -6(x + 6) = 0 6x + -2x2 + (-4 * 7 + 2x * 7) + -6(x + 6) = 0 6x + -2x2 + (-28 + 14x) + -6(x + 6) = 0 Reorder the terms: 6x + -2x2 + -28 + 14x + -6(6 + x) = 0 6x + -2x2 + -28 + 14x + (6 * -6 + x * -6) = 0 6x + -2x2 + -28 + 14x + (-36 + -6x) = 0 Reorder the terms: -28 + -36 + 6x + 14x + -6x + -2x2 = 0 Combine like terms: -28 + -36 = -64 -64 + 6x + 14x + -6x + -2x2 = 0 Combine like terms: 6x + 14x = 20x -64 + 20x + -6x + -2x2 = 0 Combine like terms: 20x + -6x = 14x -64 + 14x + -2x2 = 0 Solving -64 + 14x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + 7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying -32 + 7x + -1x2 = 0 Solving -32 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 32 + -7x + x2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -7x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -7x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -7x + x2 = 0 + -32 -7x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -7x + x2 = -32 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -32 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -32 + 12.25 Combine like terms: -32 + 12.25 = -19.75 12.25 + -7x + x2 = -19.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -19.75 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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