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Simplifying 3 + 5y(10y + (-14)) = -22 3 + 5y(10y + -14) = -22 Reorder the terms: 3 + 5y(-14 + 10y) = -22 3 + (-14 * 5y + 10y * 5y) = -22 3 + (-70y + 50y2) = -22 Solving 3 + -70y + 50y2 = -22 Solving for variable 'y'. Reorder the terms: 3 + 22 + -70y + 50y2 = -22 + 22 Combine like terms: 3 + 22 = 25 25 + -70y + 50y2 = -22 + 22 Combine like terms: -22 + 22 = 0 25 + -70y + 50y2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -14y + 10y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -14y + 10y2)' equal to zero and attempt to solve: Simplifying 5 + -14y + 10y2 = 0 Solving 5 + -14y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.5 + -1.4y + y2 = 0.0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.4y + -0.5 + y2 = 0.0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.4y + y2 = 0.0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.4y + y2 = 0.0 + -0.5 -1.4y + y2 = 0.0 + -0.5 Combine like terms: 0.0 + -0.5 = -0.5 -1.4y + y2 = -0.5 The y term is -1.4y. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4y + 0.49 + y2 = -0.5 + 0.49 Reorder the terms: 0.49 + -1.4y + y2 = -0.5 + 0.49 Combine like terms: -0.5 + 0.49 = -0.01 0.49 + -1.4y + y2 = -0.01 Factor a perfect square on the left side: (y + -0.7)(y + -0.7) = -0.01 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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