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Simplifying 4x2 + 40x + 37 = 0 Reorder the terms: 37 + 40x + 4x2 = 0 Solving 37 + 40x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9.25 + 10x + x2 = 0 Move the constant term to the right: Add '-9.25' to each side of the equation. 9.25 + 10x + -9.25 + x2 = 0 + -9.25 Reorder the terms: 9.25 + -9.25 + 10x + x2 = 0 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + 10x + x2 = 0 + -9.25 10x + x2 = 0 + -9.25 Combine like terms: 0 + -9.25 = -9.25 10x + x2 = -9.25 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -9.25 + 25 Reorder the terms: 25 + 10x + x2 = -9.25 + 25 Combine like terms: -9.25 + 25 = 15.75 25 + 10x + x2 = 15.75 Factor a perfect square on the left side: (x + 5)(x + 5) = 15.75 Calculate the square root of the right side: 3.968626967 Break this problem into two subproblems by setting (x + 5) equal to 3.968626967 and -3.968626967.Subproblem 1
x + 5 = 3.968626967 Simplifying x + 5 = 3.968626967 Reorder the terms: 5 + x = 3.968626967 Solving 5 + x = 3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 3.968626967 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.968626967 + -5 x = 3.968626967 + -5 Combine like terms: 3.968626967 + -5 = -1.031373033 x = -1.031373033 Simplifying x = -1.031373033Subproblem 2
x + 5 = -3.968626967 Simplifying x + 5 = -3.968626967 Reorder the terms: 5 + x = -3.968626967 Solving 5 + x = -3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -3.968626967 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.968626967 + -5 x = -3.968626967 + -5 Combine like terms: -3.968626967 + -5 = -8.968626967 x = -8.968626967 Simplifying x = -8.968626967Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.031373033, -8.968626967}
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