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Simplifying 4x2 + -2x(3x + 1) = 5 Reorder the terms: 4x2 + -2x(1 + 3x) = 5 4x2 + (1 * -2x + 3x * -2x) = 5 4x2 + (-2x + -6x2) = 5 Reorder the terms: -2x + 4x2 + -6x2 = 5 Combine like terms: 4x2 + -6x2 = -2x2 -2x + -2x2 = 5 Solving -2x + -2x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -2x + -2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 2x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + 2x2 = 0 Solving 5 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x + x2 = 0 + -2.5 x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 x + x2 = -2.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -2.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -2.5 + 0.25 Combine like terms: -2.5 + 0.25 = -2.25 1.25 + x2 = -2.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2.25 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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