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Simplifying 17y2 + 5y + -126 = 0 Reorder the terms: -126 + 5y + 17y2 = 0 Solving -126 + 5y + 17y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -7.411764706 + 0.2941176471y + y2 = 0 Move the constant term to the right: Add '7.411764706' to each side of the equation. -7.411764706 + 0.2941176471y + 7.411764706 + y2 = 0 + 7.411764706 Reorder the terms: -7.411764706 + 7.411764706 + 0.2941176471y + y2 = 0 + 7.411764706 Combine like terms: -7.411764706 + 7.411764706 = 0.000000000 0.000000000 + 0.2941176471y + y2 = 0 + 7.411764706 0.2941176471y + y2 = 0 + 7.411764706 Combine like terms: 0 + 7.411764706 = 7.411764706 0.2941176471y + y2 = 7.411764706 The y term is 0.2941176471y. Take half its coefficient (0.1470588236). Square it (0.02162629760) and add it to both sides. Add '0.02162629760' to each side of the equation. 0.2941176471y + 0.02162629760 + y2 = 7.411764706 + 0.02162629760 Reorder the terms: 0.02162629760 + 0.2941176471y + y2 = 7.411764706 + 0.02162629760 Combine like terms: 7.411764706 + 0.02162629760 = 7.4333910036 0.02162629760 + 0.2941176471y + y2 = 7.4333910036 Factor a perfect square on the left side: (y + 0.1470588236)(y + 0.1470588236) = 7.4333910036 Calculate the square root of the right side: 2.726424582 Break this problem into two subproblems by setting (y + 0.1470588236) equal to 2.726424582 and -2.726424582.Subproblem 1
y + 0.1470588236 = 2.726424582 Simplifying y + 0.1470588236 = 2.726424582 Reorder the terms: 0.1470588236 + y = 2.726424582 Solving 0.1470588236 + y = 2.726424582 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1470588236' to each side of the equation. 0.1470588236 + -0.1470588236 + y = 2.726424582 + -0.1470588236 Combine like terms: 0.1470588236 + -0.1470588236 = 0.0000000000 0.0000000000 + y = 2.726424582 + -0.1470588236 y = 2.726424582 + -0.1470588236 Combine like terms: 2.726424582 + -0.1470588236 = 2.5793657584 y = 2.5793657584 Simplifying y = 2.5793657584Subproblem 2
y + 0.1470588236 = -2.726424582 Simplifying y + 0.1470588236 = -2.726424582 Reorder the terms: 0.1470588236 + y = -2.726424582 Solving 0.1470588236 + y = -2.726424582 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1470588236' to each side of the equation. 0.1470588236 + -0.1470588236 + y = -2.726424582 + -0.1470588236 Combine like terms: 0.1470588236 + -0.1470588236 = 0.0000000000 0.0000000000 + y = -2.726424582 + -0.1470588236 y = -2.726424582 + -0.1470588236 Combine like terms: -2.726424582 + -0.1470588236 = -2.8734834056 y = -2.8734834056 Simplifying y = -2.8734834056Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.5793657584, -2.8734834056}
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