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Simplifying 2y2 + -8y + 12 + -13y2 + -8y + 3 = 0 Reorder the terms: 12 + 3 + -8y + -8y + 2y2 + -13y2 = 0 Combine like terms: 12 + 3 = 15 15 + -8y + -8y + 2y2 + -13y2 = 0 Combine like terms: -8y + -8y = -16y 15 + -16y + 2y2 + -13y2 = 0 Combine like terms: 2y2 + -13y2 = -11y2 15 + -16y + -11y2 = 0 Solving 15 + -16y + -11y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -1.363636364 + 1.454545455y + y2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + 1.454545455y + 1.363636364 + y2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + 1.454545455y + y2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + 1.454545455y + y2 = 0 + 1.363636364 1.454545455y + y2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 1.454545455y + y2 = 1.363636364 The y term is 1.454545455y. Take half its coefficient (0.7272727275). Square it (0.5289256202) and add it to both sides. Add '0.5289256202' to each side of the equation. 1.454545455y + 0.5289256202 + y2 = 1.363636364 + 0.5289256202 Reorder the terms: 0.5289256202 + 1.454545455y + y2 = 1.363636364 + 0.5289256202 Combine like terms: 1.363636364 + 0.5289256202 = 1.8925619842 0.5289256202 + 1.454545455y + y2 = 1.8925619842 Factor a perfect square on the left side: (y + 0.7272727275)(y + 0.7272727275) = 1.8925619842 Calculate the square root of the right side: 1.375704178 Break this problem into two subproblems by setting (y + 0.7272727275) equal to 1.375704178 and -1.375704178.Subproblem 1
y + 0.7272727275 = 1.375704178 Simplifying y + 0.7272727275 = 1.375704178 Reorder the terms: 0.7272727275 + y = 1.375704178 Solving 0.7272727275 + y = 1.375704178 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7272727275' to each side of the equation. 0.7272727275 + -0.7272727275 + y = 1.375704178 + -0.7272727275 Combine like terms: 0.7272727275 + -0.7272727275 = 0.0000000000 0.0000000000 + y = 1.375704178 + -0.7272727275 y = 1.375704178 + -0.7272727275 Combine like terms: 1.375704178 + -0.7272727275 = 0.6484314505 y = 0.6484314505 Simplifying y = 0.6484314505Subproblem 2
y + 0.7272727275 = -1.375704178 Simplifying y + 0.7272727275 = -1.375704178 Reorder the terms: 0.7272727275 + y = -1.375704178 Solving 0.7272727275 + y = -1.375704178 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7272727275' to each side of the equation. 0.7272727275 + -0.7272727275 + y = -1.375704178 + -0.7272727275 Combine like terms: 0.7272727275 + -0.7272727275 = 0.0000000000 0.0000000000 + y = -1.375704178 + -0.7272727275 y = -1.375704178 + -0.7272727275 Combine like terms: -1.375704178 + -0.7272727275 = -2.1029769055 y = -2.1029769055 Simplifying y = -2.1029769055Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.6484314505, -2.1029769055}
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