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Simplifying 7y2 + 15y + -9 = 0 Reorder the terms: -9 + 15y + 7y2 = 0 Solving -9 + 15y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + 2.142857143y + y2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 2.142857143y + 1.285714286 + y2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 2.142857143y + y2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 2.142857143y + y2 = 0 + 1.285714286 2.142857143y + y2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 2.142857143y + y2 = 1.285714286 The y term is 2.142857143y. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143y + 1.147959185 + y2 = 1.285714286 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143y + y2 = 1.285714286 + 1.147959185 Combine like terms: 1.285714286 + 1.147959185 = 2.433673471 1.147959185 + 2.142857143y + y2 = 2.433673471 Factor a perfect square on the left side: (y + 1.071428572)(y + 1.071428572) = 2.433673471 Calculate the square root of the right side: 1.560023548 Break this problem into two subproblems by setting (y + 1.071428572) equal to 1.560023548 and -1.560023548.Subproblem 1
y + 1.071428572 = 1.560023548 Simplifying y + 1.071428572 = 1.560023548 Reorder the terms: 1.071428572 + y = 1.560023548 Solving 1.071428572 + y = 1.560023548 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + y = 1.560023548 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + y = 1.560023548 + -1.071428572 y = 1.560023548 + -1.071428572 Combine like terms: 1.560023548 + -1.071428572 = 0.488594976 y = 0.488594976 Simplifying y = 0.488594976Subproblem 2
y + 1.071428572 = -1.560023548 Simplifying y + 1.071428572 = -1.560023548 Reorder the terms: 1.071428572 + y = -1.560023548 Solving 1.071428572 + y = -1.560023548 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + y = -1.560023548 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + y = -1.560023548 + -1.071428572 y = -1.560023548 + -1.071428572 Combine like terms: -1.560023548 + -1.071428572 = -2.63145212 y = -2.63145212 Simplifying y = -2.63145212Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.488594976, -2.63145212}
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