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Simplifying -4y2 + -7y = -10 Reorder the terms: -7y + -4y2 = -10 Solving -7y + -4y2 = -10 Solving for variable 'y'. Reorder the terms: 10 + -7y + -4y2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -7y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.5 + 1.75y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 1.75y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 1.75y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 1.75y + y2 = 0 + 2.5 1.75y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 1.75y + y2 = 2.5 The y term is 1.75y. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75y + 0.765625 + y2 = 2.5 + 0.765625 Reorder the terms: 0.765625 + 1.75y + y2 = 2.5 + 0.765625 Combine like terms: 2.5 + 0.765625 = 3.265625 0.765625 + 1.75y + y2 = 3.265625 Factor a perfect square on the left side: (y + 0.875)(y + 0.875) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (y + 0.875) equal to 1.807104037 and -1.807104037.Subproblem 1
y + 0.875 = 1.807104037 Simplifying y + 0.875 = 1.807104037 Reorder the terms: 0.875 + y = 1.807104037 Solving 0.875 + y = 1.807104037 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = 1.807104037 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = 1.807104037 + -0.875 y = 1.807104037 + -0.875 Combine like terms: 1.807104037 + -0.875 = 0.932104037 y = 0.932104037 Simplifying y = 0.932104037Subproblem 2
y + 0.875 = -1.807104037 Simplifying y + 0.875 = -1.807104037 Reorder the terms: 0.875 + y = -1.807104037 Solving 0.875 + y = -1.807104037 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = -1.807104037 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = -1.807104037 + -0.875 y = -1.807104037 + -0.875 Combine like terms: -1.807104037 + -0.875 = -2.682104037 y = -2.682104037 Simplifying y = -2.682104037Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.932104037, -2.682104037}
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