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Simplifying -10y + 18 = 3(5y + -7) * 5y Reorder the terms: 18 + -10y = 3(5y + -7) * 5y Reorder the terms: 18 + -10y = 3(-7 + 5y) * 5y Reorder the terms for easier multiplication: 18 + -10y = 3 * 5y(-7 + 5y) Multiply 3 * 5 18 + -10y = 15y(-7 + 5y) 18 + -10y = (-7 * 15y + 5y * 15y) 18 + -10y = (-105y + 75y2) Solving 18 + -10y = -105y + 75y2 Solving for variable 'y'. Combine like terms: -10y + 105y = 95y 18 + 95y + -75y2 = -105y + 75y2 + 105y + -75y2 Reorder the terms: 18 + 95y + -75y2 = -105y + 105y + 75y2 + -75y2 Combine like terms: -105y + 105y = 0 18 + 95y + -75y2 = 0 + 75y2 + -75y2 18 + 95y + -75y2 = 75y2 + -75y2 Combine like terms: 75y2 + -75y2 = 0 18 + 95y + -75y2 = 0 Begin completing the square. Divide all terms by -75 the coefficient of the squared term: Divide each side by '-75'. -0.24 + -1.266666667y + y2 = 0 Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + -1.266666667y + 0.24 + y2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + -1.266666667y + y2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + -1.266666667y + y2 = 0 + 0.24 -1.266666667y + y2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 -1.266666667y + y2 = 0.24 The y term is -1.266666667y. Take half its coefficient (-0.6333333335). Square it (0.4011111113) and add it to both sides. Add '0.4011111113' to each side of the equation. -1.266666667y + 0.4011111113 + y2 = 0.24 + 0.4011111113 Reorder the terms: 0.4011111113 + -1.266666667y + y2 = 0.24 + 0.4011111113 Combine like terms: 0.24 + 0.4011111113 = 0.6411111113 0.4011111113 + -1.266666667y + y2 = 0.6411111113 Factor a perfect square on the left side: (y + -0.6333333335)(y + -0.6333333335) = 0.6411111113 Calculate the square root of the right side: 0.800694143 Break this problem into two subproblems by setting (y + -0.6333333335) equal to 0.800694143 and -0.800694143.Subproblem 1
y + -0.6333333335 = 0.800694143 Simplifying y + -0.6333333335 = 0.800694143 Reorder the terms: -0.6333333335 + y = 0.800694143 Solving -0.6333333335 + y = 0.800694143 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6333333335' to each side of the equation. -0.6333333335 + 0.6333333335 + y = 0.800694143 + 0.6333333335 Combine like terms: -0.6333333335 + 0.6333333335 = 0.0000000000 0.0000000000 + y = 0.800694143 + 0.6333333335 y = 0.800694143 + 0.6333333335 Combine like terms: 0.800694143 + 0.6333333335 = 1.4340274765 y = 1.4340274765 Simplifying y = 1.4340274765Subproblem 2
y + -0.6333333335 = -0.800694143 Simplifying y + -0.6333333335 = -0.800694143 Reorder the terms: -0.6333333335 + y = -0.800694143 Solving -0.6333333335 + y = -0.800694143 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6333333335' to each side of the equation. -0.6333333335 + 0.6333333335 + y = -0.800694143 + 0.6333333335 Combine like terms: -0.6333333335 + 0.6333333335 = 0.0000000000 0.0000000000 + y = -0.800694143 + 0.6333333335 y = -0.800694143 + 0.6333333335 Combine like terms: -0.800694143 + 0.6333333335 = -0.1673608095 y = -0.1673608095 Simplifying y = -0.1673608095Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.4340274765, -0.1673608095}
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