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Simplifying 7y(5y + -10) = 28 Reorder the terms: 7y(-10 + 5y) = 28 (-10 * 7y + 5y * 7y) = 28 (-70y + 35y2) = 28 Solving -70y + 35y2 = 28 Solving for variable 'y'. Reorder the terms: -28 + -70y + 35y2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -70y + 35y2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-4 + -10y + 5y2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-4 + -10y + 5y2)' equal to zero and attempt to solve: Simplifying -4 + -10y + 5y2 = 0 Solving -4 + -10y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -2y + y2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -2y + 0.8 + y2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -2y + y2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -2y + y2 = 0 + 0.8 -2y + y2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -2y + y2 = 0.8 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 0.8 + 1 Reorder the terms: 1 + -2y + y2 = 0.8 + 1 Combine like terms: 0.8 + 1 = 1.8 1 + -2y + y2 = 1.8 Factor a perfect square on the left side: (y + -1)(y + -1) = 1.8 Calculate the square root of the right side: 1.341640787 Break this problem into two subproblems by setting (y + -1) equal to 1.341640787 and -1.341640787.Subproblem 1
y + -1 = 1.341640787 Simplifying y + -1 = 1.341640787 Reorder the terms: -1 + y = 1.341640787 Solving -1 + y = 1.341640787 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.341640787 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.341640787 + 1 y = 1.341640787 + 1 Combine like terms: 1.341640787 + 1 = 2.341640787 y = 2.341640787 Simplifying y = 2.341640787Subproblem 2
y + -1 = -1.341640787 Simplifying y + -1 = -1.341640787 Reorder the terms: -1 + y = -1.341640787 Solving -1 + y = -1.341640787 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.341640787 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.341640787 + 1 y = -1.341640787 + 1 Combine like terms: -1.341640787 + 1 = -0.341640787 y = -0.341640787 Simplifying y = -0.341640787Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.341640787, -0.341640787}Solution
y = {2.341640787, -0.341640787}
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