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Simplifying 3(x2 + -10) + -3x = 6(x2 + -2x) Reorder the terms: 3(-10 + x2) + -3x = 6(x2 + -2x) (-10 * 3 + x2 * 3) + -3x = 6(x2 + -2x) (-30 + 3x2) + -3x = 6(x2 + -2x) Reorder the terms: -30 + -3x + 3x2 = 6(x2 + -2x) Reorder the terms: -30 + -3x + 3x2 = 6(-2x + x2) -30 + -3x + 3x2 = (-2x * 6 + x2 * 6) -30 + -3x + 3x2 = (-12x + 6x2) Solving -30 + -3x + 3x2 = -12x + 6x2 Solving for variable 'x'. Reorder the terms: -30 + -3x + 12x + 3x2 + -6x2 = -12x + 6x2 + 12x + -6x2 Combine like terms: -3x + 12x = 9x -30 + 9x + 3x2 + -6x2 = -12x + 6x2 + 12x + -6x2 Combine like terms: 3x2 + -6x2 = -3x2 -30 + 9x + -3x2 = -12x + 6x2 + 12x + -6x2 Reorder the terms: -30 + 9x + -3x2 = -12x + 12x + 6x2 + -6x2 Combine like terms: -12x + 12x = 0 -30 + 9x + -3x2 = 0 + 6x2 + -6x2 -30 + 9x + -3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -30 + 9x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 3x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -10 + 3x + -1x2 = 0 Solving -10 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -3x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -3x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -3x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x + x2 = 0 + -10 -3x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -3x + x2 = -10 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 = -10 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -10 + 2.25 Combine like terms: -10 + 2.25 = -7.75 2.25 + -3x + x2 = -7.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -7.75 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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