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Simplifying 28x2 + 148x + 520 = 0 Reorder the terms: 520 + 148x + 28x2 = 0 Solving 520 + 148x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(130 + 37x + 7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(130 + 37x + 7x2)' equal to zero and attempt to solve: Simplifying 130 + 37x + 7x2 = 0 Solving 130 + 37x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 18.57142857 + 5.285714286x + x2 = 0 Move the constant term to the right: Add '-18.57142857' to each side of the equation. 18.57142857 + 5.285714286x + -18.57142857 + x2 = 0 + -18.57142857 Reorder the terms: 18.57142857 + -18.57142857 + 5.285714286x + x2 = 0 + -18.57142857 Combine like terms: 18.57142857 + -18.57142857 = 0.00000000 0.00000000 + 5.285714286x + x2 = 0 + -18.57142857 5.285714286x + x2 = 0 + -18.57142857 Combine like terms: 0 + -18.57142857 = -18.57142857 5.285714286x + x2 = -18.57142857 The x term is 5.285714286x. Take half its coefficient (2.642857143). Square it (6.984693878) and add it to both sides. Add '6.984693878' to each side of the equation. 5.285714286x + 6.984693878 + x2 = -18.57142857 + 6.984693878 Reorder the terms: 6.984693878 + 5.285714286x + x2 = -18.57142857 + 6.984693878 Combine like terms: -18.57142857 + 6.984693878 = -11.586734692 6.984693878 + 5.285714286x + x2 = -11.586734692 Factor a perfect square on the left side: (x + 2.642857143)(x + 2.642857143) = -11.586734692 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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