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Simplifying 4x2 = 12x + -40 Reorder the terms: 4x2 = -40 + 12x Solving 4x2 = -40 + 12x Solving for variable 'x'. Reorder the terms: 40 + -12x + 4x2 = -40 + 12x + 40 + -12x Reorder the terms: 40 + -12x + 4x2 = -40 + 40 + 12x + -12x Combine like terms: -40 + 40 = 0 40 + -12x + 4x2 = 0 + 12x + -12x 40 + -12x + 4x2 = 12x + -12x Combine like terms: 12x + -12x = 0 40 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(10 + -3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(10 + -3x + x2)' equal to zero and attempt to solve: Simplifying 10 + -3x + x2 = 0 Solving 10 + -3x + x2 = 0 Begin completing the square. 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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