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Simplifying 0 = 2x2 + 3x + 7 Reorder the terms: 0 = 7 + 3x + 2x2 Solving 0 = 7 + 3x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -3x + -2x2 = 7 + 3x + 2x2 + -7 + -3x + -2x2 Reorder the terms: -7 + -3x + -2x2 = 7 + -7 + 3x + -3x + 2x2 + -2x2 Combine like terms: 7 + -7 = 0 -7 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2 -7 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 -7 + -3x + -2x2 = 0 + 2x2 + -2x2 -7 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -7 + -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 3x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + 2x2 = 0 Solving 7 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 1.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 1.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 1.5x + x2 = 0 + -3.5 1.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 1.5x + x2 = -3.5 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 = -3.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -3.5 + 0.5625 Combine like terms: -3.5 + 0.5625 = -2.9375 0.5625 + 1.5x + x2 = -2.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -2.9375 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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