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Simplifying 14x2 + 32x + 180 = 0 Reorder the terms: 180 + 32x + 14x2 = 0 Solving 180 + 32x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(90 + 16x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + 16x + 7x2)' equal to zero and attempt to solve: Simplifying 90 + 16x + 7x2 = 0 Solving 90 + 16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 12.85714286 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '-12.85714286' to each side of the equation. 12.85714286 + 2.285714286x + -12.85714286 + x2 = 0 + -12.85714286 Reorder the terms: 12.85714286 + -12.85714286 + 2.285714286x + x2 = 0 + -12.85714286 Combine like terms: 12.85714286 + -12.85714286 = 0.00000000 0.00000000 + 2.285714286x + x2 = 0 + -12.85714286 2.285714286x + x2 = 0 + -12.85714286 Combine like terms: 0 + -12.85714286 = -12.85714286 2.285714286x + x2 = -12.85714286 The x term is 2.285714286x. Take half its coefficient (1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. 2.285714286x + 1.306122449 + x2 = -12.85714286 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = -12.85714286 + 1.306122449 Combine like terms: -12.85714286 + 1.306122449 = -11.551020411 1.306122449 + 2.285714286x + x2 = -11.551020411 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = -11.551020411 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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