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Simplifying 40 = -3x2 + 42x + -110 Reorder the terms: 40 = -110 + 42x + -3x2 Solving 40 = -110 + 42x + -3x2 Solving for variable 'x'. Combine like terms: 40 + 110 = 150 150 + -42x + 3x2 = -110 + 42x + -3x2 + 110 + -42x + 3x2 Reorder the terms: 150 + -42x + 3x2 = -110 + 110 + 42x + -42x + -3x2 + 3x2 Combine like terms: -110 + 110 = 0 150 + -42x + 3x2 = 0 + 42x + -42x + -3x2 + 3x2 150 + -42x + 3x2 = 42x + -42x + -3x2 + 3x2 Combine like terms: 42x + -42x = 0 150 + -42x + 3x2 = 0 + -3x2 + 3x2 150 + -42x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 150 + -42x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(50 + -14x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(50 + -14x + x2)' equal to zero and attempt to solve: Simplifying 50 + -14x + x2 = 0 Solving 50 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -14x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -14x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -14x + x2 = 0 + -50 -14x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -14x + x2 = -50 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -50 + 49 Reorder the terms: 49 + -14x + x2 = -50 + 49 Combine like terms: -50 + 49 = -1 49 + -14x + x2 = -1 Factor a perfect square on the left side: (x + -7)(x + -7) = -1 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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