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Simplifying (y + 0.4)(y + 0.4) = 0.84 Reorder the terms: (0.4 + y)(y + 0.4) = 0.84 Reorder the terms: (0.4 + y)(0.4 + y) = 0.84 Multiply (0.4 + y) * (0.4 + y) (0.4(0.4 + y) + y(0.4 + y)) = 0.84 ((0.4 * 0.4 + y * 0.4) + y(0.4 + y)) = 0.84 ((0.16 + 0.4y) + y(0.4 + y)) = 0.84 (0.16 + 0.4y + (0.4 * y + y * y)) = 0.84 (0.16 + 0.4y + (0.4y + y2)) = 0.84 Combine like terms: 0.4y + 0.4y = 0.8y (0.16 + 0.8y + y2) = 0.84 Solving 0.16 + 0.8y + y2 = 0.84 Solving for variable 'y'. Reorder the terms: 0.16 + -0.84 + 0.8y + y2 = 0.84 + -0.84 Combine like terms: 0.16 + -0.84 = -0.68 -0.68 + 0.8y + y2 = 0.84 + -0.84 Combine like terms: 0.84 + -0.84 = 0.00 -0.68 + 0.8y + y2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.68' to each side of the equation. -0.68 + 0.8y + 0.68 + y2 = 0.00 + 0.68 Reorder the terms: -0.68 + 0.68 + 0.8y + y2 = 0.00 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + 0.8y + y2 = 0.00 + 0.68 0.8y + y2 = 0.00 + 0.68 Combine like terms: 0.00 + 0.68 = 0.68 0.8y + y2 = 0.68 The y term is 0.8y. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8y + 0.16 + y2 = 0.68 + 0.16 Reorder the terms: 0.16 + 0.8y + y2 = 0.68 + 0.16 Combine like terms: 0.68 + 0.16 = 0.84 0.16 + 0.8y + y2 = 0.84 Factor a perfect square on the left side: (y + 0.4)(y + 0.4) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (y + 0.4) equal to 0.916515139 and -0.916515139.Subproblem 1
y + 0.4 = 0.916515139 Simplifying y + 0.4 = 0.916515139 Reorder the terms: 0.4 + y = 0.916515139 Solving 0.4 + y = 0.916515139 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = 0.916515139 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 0.916515139 + -0.4 y = 0.916515139 + -0.4 Combine like terms: 0.916515139 + -0.4 = 0.516515139 y = 0.516515139 Simplifying y = 0.516515139Subproblem 2
y + 0.4 = -0.916515139 Simplifying y + 0.4 = -0.916515139 Reorder the terms: 0.4 + y = -0.916515139 Solving 0.4 + y = -0.916515139 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = -0.916515139 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -0.916515139 + -0.4 y = -0.916515139 + -0.4 Combine like terms: -0.916515139 + -0.4 = -1.316515139 y = -1.316515139 Simplifying y = -1.316515139Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.516515139, -1.316515139}
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