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Simplifying -1(x) = 4x2 + 5x + 7 Reorder the terms: -1x = 7 + 5x + 4x2 Solving -1x = 7 + 5x + 4x2 Solving for variable 'x'. Reorder the terms: -7 + -1x + -5x + -4x2 = 7 + 5x + 4x2 + -7 + -5x + -4x2 Combine like terms: -1x + -5x = -6x -7 + -6x + -4x2 = 7 + 5x + 4x2 + -7 + -5x + -4x2 Reorder the terms: -7 + -6x + -4x2 = 7 + -7 + 5x + -5x + 4x2 + -4x2 Combine like terms: 7 + -7 = 0 -7 + -6x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2 -7 + -6x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 -7 + -6x + -4x2 = 0 + 4x2 + -4x2 -7 + -6x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -7 + -6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 6x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 6x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + 6x + 4x2 = 0 Solving 7 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 1.5x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 1.5x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 1.5x + x2 = 0 + -1.75 1.5x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 1.5x + x2 = -1.75 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -1.75 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1.75 + 0.5625 Combine like terms: -1.75 + 0.5625 = -1.1875 0.5625 + 1.5x + x2 = -1.1875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -1.1875 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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