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Simplifying y2 + 1.4y + 0.49 + -36y2 = 0 Reorder the terms: 0.49 + 1.4y + y2 + -36y2 = 0 Combine like terms: y2 + -36y2 = -35y2 0.49 + 1.4y + -35y2 = 0 Solving 0.49 + 1.4y + -35y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -0.014 + -0.04y + y2 = 0 Move the constant term to the right: Add '0.014' to each side of the equation. -0.014 + -0.04y + 0.014 + y2 = 0 + 0.014 Reorder the terms: -0.014 + 0.014 + -0.04y + y2 = 0 + 0.014 Combine like terms: -0.014 + 0.014 = 0.000 0.000 + -0.04y + y2 = 0 + 0.014 -0.04y + y2 = 0 + 0.014 Combine like terms: 0 + 0.014 = 0.014 -0.04y + y2 = 0.014 The y term is -0.04y. Take half its coefficient (-0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. -0.04y + 0.0004 + y2 = 0.014 + 0.0004 Reorder the terms: 0.0004 + -0.04y + y2 = 0.014 + 0.0004 Combine like terms: 0.014 + 0.0004 = 0.0144 0.0004 + -0.04y + y2 = 0.0144 Factor a perfect square on the left side: (y + -0.02)(y + -0.02) = 0.0144 Calculate the square root of the right side: 0.12 Break this problem into two subproblems by setting (y + -0.02) equal to 0.12 and -0.12.Subproblem 1
y + -0.02 = 0.12 Simplifying y + -0.02 = 0.12 Reorder the terms: -0.02 + y = 0.12 Solving -0.02 + y = 0.12 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + y = 0.12 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + y = 0.12 + 0.02 y = 0.12 + 0.02 Combine like terms: 0.12 + 0.02 = 0.14 y = 0.14 Simplifying y = 0.14Subproblem 2
y + -0.02 = -0.12 Simplifying y + -0.02 = -0.12 Reorder the terms: -0.02 + y = -0.12 Solving -0.02 + y = -0.12 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + y = -0.12 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + y = -0.12 + 0.02 y = -0.12 + 0.02 Combine like terms: -0.12 + 0.02 = -0.1 y = -0.1 Simplifying y = -0.1Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.14, -0.1}
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