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Simplifying x = 7x2 + 3x + 7 Reorder the terms: x = 7 + 3x + 7x2 Solving x = 7 + 3x + 7x2 Solving for variable 'x'. Reorder the terms: -7 + x + -3x + -7x2 = 7 + 3x + 7x2 + -7 + -3x + -7x2 Combine like terms: x + -3x = -2x -7 + -2x + -7x2 = 7 + 3x + 7x2 + -7 + -3x + -7x2 Reorder the terms: -7 + -2x + -7x2 = 7 + -7 + 3x + -3x + 7x2 + -7x2 Combine like terms: 7 + -7 = 0 -7 + -2x + -7x2 = 0 + 3x + -3x + 7x2 + -7x2 -7 + -2x + -7x2 = 3x + -3x + 7x2 + -7x2 Combine like terms: 3x + -3x = 0 -7 + -2x + -7x2 = 0 + 7x2 + -7x2 -7 + -2x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -7 + -2x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 2x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 2x + 7x2)' equal to zero and attempt to solve: Simplifying 7 + 2x + 7x2 = 0 Solving 7 + 2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.2857142857x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 0.2857142857x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.2857142857x + x2 = 0 + -1 0.2857142857x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.2857142857x + x2 = -1 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = -1 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = -1 + 0.02040816328 Combine like terms: -1 + 0.02040816328 = -0.97959183672 0.02040816328 + 0.2857142857x + x2 = -0.97959183672 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = -0.97959183672 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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