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Simplifying (x + -10)(3x + 12) = 3x + -900 Reorder the terms: (-10 + x)(3x + 12) = 3x + -900 Reorder the terms: (-10 + x)(12 + 3x) = 3x + -900 Multiply (-10 + x) * (12 + 3x) (-10(12 + 3x) + x(12 + 3x)) = 3x + -900 ((12 * -10 + 3x * -10) + x(12 + 3x)) = 3x + -900 ((-120 + -30x) + x(12 + 3x)) = 3x + -900 (-120 + -30x + (12 * x + 3x * x)) = 3x + -900 (-120 + -30x + (12x + 3x2)) = 3x + -900 Combine like terms: -30x + 12x = -18x (-120 + -18x + 3x2) = 3x + -900 Reorder the terms: -120 + -18x + 3x2 = -900 + 3x Solving -120 + -18x + 3x2 = -900 + 3x Solving for variable 'x'. Reorder the terms: -120 + 900 + -18x + -3x + 3x2 = -900 + 3x + 900 + -3x Combine like terms: -120 + 900 = 780 780 + -18x + -3x + 3x2 = -900 + 3x + 900 + -3x Combine like terms: -18x + -3x = -21x 780 + -21x + 3x2 = -900 + 3x + 900 + -3x Reorder the terms: 780 + -21x + 3x2 = -900 + 900 + 3x + -3x Combine like terms: -900 + 900 = 0 780 + -21x + 3x2 = 0 + 3x + -3x 780 + -21x + 3x2 = 3x + -3x Combine like terms: 3x + -3x = 0 780 + -21x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(260 + -7x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(260 + -7x + x2)' equal to zero and attempt to solve: Simplifying 260 + -7x + x2 = 0 Solving 260 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-260' to each side of the equation. 260 + -7x + -260 + x2 = 0 + -260 Reorder the terms: 260 + -260 + -7x + x2 = 0 + -260 Combine like terms: 260 + -260 = 0 0 + -7x + x2 = 0 + -260 -7x + x2 = 0 + -260 Combine like terms: 0 + -260 = -260 -7x + x2 = -260 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 = -260 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -260 + 12.25 Combine like terms: -260 + 12.25 = -247.75 12.25 + -7x + x2 = -247.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -247.75 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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