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Simplifying 5(y2 + -14y + 49) = -90 Reorder the terms: 5(49 + -14y + y2) = -90 (49 * 5 + -14y * 5 + y2 * 5) = -90 (245 + -70y + 5y2) = -90 Solving 245 + -70y + 5y2 = -90 Solving for variable 'y'. Reorder the terms: 245 + 90 + -70y + 5y2 = -90 + 90 Combine like terms: 245 + 90 = 335 335 + -70y + 5y2 = -90 + 90 Combine like terms: -90 + 90 = 0 335 + -70y + 5y2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(67 + -14y + y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(67 + -14y + y2)' equal to zero and attempt to solve: Simplifying 67 + -14y + y2 = 0 Solving 67 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-67' to each side of the equation. 67 + -14y + -67 + y2 = 0 + -67 Reorder the terms: 67 + -67 + -14y + y2 = 0 + -67 Combine like terms: 67 + -67 = 0 0 + -14y + y2 = 0 + -67 -14y + y2 = 0 + -67 Combine like terms: 0 + -67 = -67 -14y + y2 = -67 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -67 + 49 Reorder the terms: 49 + -14y + y2 = -67 + 49 Combine like terms: -67 + 49 = -18 49 + -14y + y2 = -18 Factor a perfect square on the left side: (y + -7)(y + -7) = -18 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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