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Simplifying -10y + 18 = -3y(5y + -7) + 5y Reorder the terms: 18 + -10y = -3y(5y + -7) + 5y Reorder the terms: 18 + -10y = -3y(-7 + 5y) + 5y 18 + -10y = (-7 * -3y + 5y * -3y) + 5y 18 + -10y = (21y + -15y2) + 5y Reorder the terms: 18 + -10y = 21y + 5y + -15y2 Combine like terms: 21y + 5y = 26y 18 + -10y = 26y + -15y2 Solving 18 + -10y = 26y + -15y2 Solving for variable 'y'. Combine like terms: -10y + -26y = -36y 18 + -36y + 15y2 = 26y + -15y2 + -26y + 15y2 Reorder the terms: 18 + -36y + 15y2 = 26y + -26y + -15y2 + 15y2 Combine like terms: 26y + -26y = 0 18 + -36y + 15y2 = 0 + -15y2 + 15y2 18 + -36y + 15y2 = -15y2 + 15y2 Combine like terms: -15y2 + 15y2 = 0 18 + -36y + 15y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -12y + 5y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -12y + 5y2)' equal to zero and attempt to solve: Simplifying 6 + -12y + 5y2 = 0 Solving 6 + -12y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -2.4y + y2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -2.4y + -1.2 + y2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -2.4y + y2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -2.4y + y2 = 0 + -1.2 -2.4y + y2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -2.4y + y2 = -1.2 The y term is -2.4y. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4y + 1.44 + y2 = -1.2 + 1.44 Reorder the terms: 1.44 + -2.4y + y2 = -1.2 + 1.44 Combine like terms: -1.2 + 1.44 = 0.24 1.44 + -2.4y + y2 = 0.24 Factor a perfect square on the left side: (y + -1.2)(y + -1.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (y + -1.2) equal to 0.489897949 and -0.489897949.Subproblem 1
y + -1.2 = 0.489897949 Simplifying y + -1.2 = 0.489897949 Reorder the terms: -1.2 + y = 0.489897949 Solving -1.2 + y = 0.489897949 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + y = 0.489897949 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + y = 0.489897949 + 1.2 y = 0.489897949 + 1.2 Combine like terms: 0.489897949 + 1.2 = 1.689897949 y = 1.689897949 Simplifying y = 1.689897949Subproblem 2
y + -1.2 = -0.489897949 Simplifying y + -1.2 = -0.489897949 Reorder the terms: -1.2 + y = -0.489897949 Solving -1.2 + y = -0.489897949 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + y = -0.489897949 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + y = -0.489897949 + 1.2 y = -0.489897949 + 1.2 Combine like terms: -0.489897949 + 1.2 = 0.710102051 y = 0.710102051 Simplifying y = 0.710102051Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.689897949, 0.710102051}Solution
y = {1.689897949, 0.710102051}
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