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Simplifying 18y * 18y + -18y + -16y * 16y + 12y + -15 = 0 Reorder the terms for easier multiplication: 18 * 18y * y + -18y + -16y * 16y + 12y + -15 = 0 Multiply 18 * 18 324y * y + -18y + -16y * 16y + 12y + -15 = 0 Multiply y * y 324y2 + -18y + -16y * 16y + 12y + -15 = 0 Reorder the terms for easier multiplication: 324y2 + -18y + -16 * 16y * y + 12y + -15 = 0 Multiply -16 * 16 324y2 + -18y + -256y * y + 12y + -15 = 0 Multiply y * y 324y2 + -18y + -256y2 + 12y + -15 = 0 Reorder the terms: -15 + -18y + 12y + 324y2 + -256y2 = 0 Combine like terms: -18y + 12y = -6y -15 + -6y + 324y2 + -256y2 = 0 Combine like terms: 324y2 + -256y2 = 68y2 -15 + -6y + 68y2 = 0 Solving -15 + -6y + 68y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 68 the coefficient of the squared term: Divide each side by '68'. -0.2205882353 + -0.08823529412y + y2 = 0 Move the constant term to the right: Add '0.2205882353' to each side of the equation. -0.2205882353 + -0.08823529412y + 0.2205882353 + y2 = 0 + 0.2205882353 Reorder the terms: -0.2205882353 + 0.2205882353 + -0.08823529412y + y2 = 0 + 0.2205882353 Combine like terms: -0.2205882353 + 0.2205882353 = 0.0000000000 0.0000000000 + -0.08823529412y + y2 = 0 + 0.2205882353 -0.08823529412y + y2 = 0 + 0.2205882353 Combine like terms: 0 + 0.2205882353 = 0.2205882353 -0.08823529412y + y2 = 0.2205882353 The y term is -0.08823529412y. Take half its coefficient (-0.04411764706). Square it (0.001946366782) and add it to both sides. Add '0.001946366782' to each side of the equation. -0.08823529412y + 0.001946366782 + y2 = 0.2205882353 + 0.001946366782 Reorder the terms: 0.001946366782 + -0.08823529412y + y2 = 0.2205882353 + 0.001946366782 Combine like terms: 0.2205882353 + 0.001946366782 = 0.222534602082 0.001946366782 + -0.08823529412y + y2 = 0.222534602082 Factor a perfect square on the left side: (y + -0.04411764706)(y + -0.04411764706) = 0.222534602082 Calculate the square root of the right side: 0.471735733 Break this problem into two subproblems by setting (y + -0.04411764706) equal to 0.471735733 and -0.471735733.Subproblem 1
y + -0.04411764706 = 0.471735733 Simplifying y + -0.04411764706 = 0.471735733 Reorder the terms: -0.04411764706 + y = 0.471735733 Solving -0.04411764706 + y = 0.471735733 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.04411764706' to each side of the equation. -0.04411764706 + 0.04411764706 + y = 0.471735733 + 0.04411764706 Combine like terms: -0.04411764706 + 0.04411764706 = 0.00000000000 0.00000000000 + y = 0.471735733 + 0.04411764706 y = 0.471735733 + 0.04411764706 Combine like terms: 0.471735733 + 0.04411764706 = 0.51585338006 y = 0.51585338006 Simplifying y = 0.51585338006Subproblem 2
y + -0.04411764706 = -0.471735733 Simplifying y + -0.04411764706 = -0.471735733 Reorder the terms: -0.04411764706 + y = -0.471735733 Solving -0.04411764706 + y = -0.471735733 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.04411764706' to each side of the equation. -0.04411764706 + 0.04411764706 + y = -0.471735733 + 0.04411764706 Combine like terms: -0.04411764706 + 0.04411764706 = 0.00000000000 0.00000000000 + y = -0.471735733 + 0.04411764706 y = -0.471735733 + 0.04411764706 Combine like terms: -0.471735733 + 0.04411764706 = -0.42761808594 y = -0.42761808594 Simplifying y = -0.42761808594Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.51585338006, -0.42761808594}
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