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Simplifying (0.7 + -1y) * y = 0.08 Reorder the terms for easier multiplication: y(0.7 + -1y) = 0.08 (0.7 * y + -1y * y) = 0.08 (0.7y + -1y2) = 0.08 Solving 0.7y + -1y2 = 0.08 Solving for variable 'y'. Reorder the terms: -0.08 + 0.7y + -1y2 = 0.08 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 -0.08 + 0.7y + -1y2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.08 + -0.7y + y2 = 0.00 Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + -0.7y + -0.08 + y2 = 0.00 + -0.08 Reorder the terms: 0.08 + -0.08 + -0.7y + y2 = 0.00 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + -0.7y + y2 = 0.00 + -0.08 -0.7y + y2 = 0.00 + -0.08 Combine like terms: 0.00 + -0.08 = -0.08 -0.7y + y2 = -0.08 The y term is -0.7y. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7y + 0.1225 + y2 = -0.08 + 0.1225 Reorder the terms: 0.1225 + -0.7y + y2 = -0.08 + 0.1225 Combine like terms: -0.08 + 0.1225 = 0.0425 0.1225 + -0.7y + y2 = 0.0425 Factor a perfect square on the left side: (y + -0.35)(y + -0.35) = 0.0425 Calculate the square root of the right side: 0.206155281 Break this problem into two subproblems by setting (y + -0.35) equal to 0.206155281 and -0.206155281.Subproblem 1
y + -0.35 = 0.206155281 Simplifying y + -0.35 = 0.206155281 Reorder the terms: -0.35 + y = 0.206155281 Solving -0.35 + y = 0.206155281 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + y = 0.206155281 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + y = 0.206155281 + 0.35 y = 0.206155281 + 0.35 Combine like terms: 0.206155281 + 0.35 = 0.556155281 y = 0.556155281 Simplifying y = 0.556155281Subproblem 2
y + -0.35 = -0.206155281 Simplifying y + -0.35 = -0.206155281 Reorder the terms: -0.35 + y = -0.206155281 Solving -0.35 + y = -0.206155281 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + y = -0.206155281 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + y = -0.206155281 + 0.35 y = -0.206155281 + 0.35 Combine like terms: -0.206155281 + 0.35 = 0.143844719 y = 0.143844719 Simplifying y = 0.143844719Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.556155281, 0.143844719}
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