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Simplifying 4y(17y + -9) = 180 Reorder the terms: 4y(-9 + 17y) = 180 (-9 * 4y + 17y * 4y) = 180 (-36y + 68y2) = 180 Solving -36y + 68y2 = 180 Solving for variable 'y'. Reorder the terms: -180 + -36y + 68y2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -36y + 68y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + -9y + 17y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + -9y + 17y2)' equal to zero and attempt to solve: Simplifying -45 + -9y + 17y2 = 0 Solving -45 + -9y + 17y2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -2.647058824 + -0.5294117647y + y2 = 0 Move the constant term to the right: Add '2.647058824' to each side of the equation. -2.647058824 + -0.5294117647y + 2.647058824 + y2 = 0 + 2.647058824 Reorder the terms: -2.647058824 + 2.647058824 + -0.5294117647y + y2 = 0 + 2.647058824 Combine like terms: -2.647058824 + 2.647058824 = 0.000000000 0.000000000 + -0.5294117647y + y2 = 0 + 2.647058824 -0.5294117647y + y2 = 0 + 2.647058824 Combine like terms: 0 + 2.647058824 = 2.647058824 -0.5294117647y + y2 = 2.647058824 The y term is -0.5294117647y. Take half its coefficient (-0.2647058824). Square it (0.07006920418) and add it to both sides. Add '0.07006920418' to each side of the equation. -0.5294117647y + 0.07006920418 + y2 = 2.647058824 + 0.07006920418 Reorder the terms: 0.07006920418 + -0.5294117647y + y2 = 2.647058824 + 0.07006920418 Combine like terms: 2.647058824 + 0.07006920418 = 2.71712802818 0.07006920418 + -0.5294117647y + y2 = 2.71712802818 Factor a perfect square on the left side: (y + -0.2647058824)(y + -0.2647058824) = 2.71712802818 Calculate the square root of the right side: 1.648371326 Break this problem into two subproblems by setting (y + -0.2647058824) equal to 1.648371326 and -1.648371326.Subproblem 1
y + -0.2647058824 = 1.648371326 Simplifying y + -0.2647058824 = 1.648371326 Reorder the terms: -0.2647058824 + y = 1.648371326 Solving -0.2647058824 + y = 1.648371326 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2647058824' to each side of the equation. -0.2647058824 + 0.2647058824 + y = 1.648371326 + 0.2647058824 Combine like terms: -0.2647058824 + 0.2647058824 = 0.0000000000 0.0000000000 + y = 1.648371326 + 0.2647058824 y = 1.648371326 + 0.2647058824 Combine like terms: 1.648371326 + 0.2647058824 = 1.9130772084 y = 1.9130772084 Simplifying y = 1.9130772084Subproblem 2
y + -0.2647058824 = -1.648371326 Simplifying y + -0.2647058824 = -1.648371326 Reorder the terms: -0.2647058824 + y = -1.648371326 Solving -0.2647058824 + y = -1.648371326 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2647058824' to each side of the equation. -0.2647058824 + 0.2647058824 + y = -1.648371326 + 0.2647058824 Combine like terms: -0.2647058824 + 0.2647058824 = 0.0000000000 0.0000000000 + y = -1.648371326 + 0.2647058824 y = -1.648371326 + 0.2647058824 Combine like terms: -1.648371326 + 0.2647058824 = -1.3836654436 y = -1.3836654436 Simplifying y = -1.3836654436Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.9130772084, -1.3836654436}Solution
y = {1.9130772084, -1.3836654436}
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