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Simplifying 4x3 + 4x2 + 7x + 1 = 1 Reorder the terms: 1 + 7x + 4x2 + 4x3 = 1 Add '-1' to each side of the equation. 1 + 7x + 4x2 + -1 + 4x3 = 1 + -1 Reorder the terms: 1 + -1 + 7x + 4x2 + 4x3 = 1 + -1 Combine like terms: 1 + -1 = 0 0 + 7x + 4x2 + 4x3 = 1 + -1 7x + 4x2 + 4x3 = 1 + -1 Combine like terms: 1 + -1 = 0 7x + 4x2 + 4x3 = 0 Solving 7x + 4x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(7 + 4x + 4x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + 4x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + 4x + 4x2 = 0 Solving 7 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x + x2 = 0 + -1.75 x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 x + x2 = -1.75 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 = -1.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -1.75 + 0.25 Combine like terms: -1.75 + 0.25 = -1.5 1.25 + x2 = -1.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.5 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.Solution
x = {0}
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