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Simplifying 9x2 + 37x + 36 = 0 Reorder the terms: 36 + 37x + 9x2 = 0 Solving 36 + 37x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4 + 4.111111111x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.111111111x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 4.111111111x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.111111111x + x2 = 0 + -4 4.111111111x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.111111111x + x2 = -4 The x term is 4.111111111x. Take half its coefficient (2.055555556). Square it (4.225308644) and add it to both sides. Add '4.225308644' to each side of the equation. 4.111111111x + 4.225308644 + x2 = -4 + 4.225308644 Reorder the terms: 4.225308644 + 4.111111111x + x2 = -4 + 4.225308644 Combine like terms: -4 + 4.225308644 = 0.225308644 4.225308644 + 4.111111111x + x2 = 0.225308644 Factor a perfect square on the left side: (x + 2.055555556)(x + 2.055555556) = 0.225308644 Calculate the square root of the right side: 0.474666877 Break this problem into two subproblems by setting (x + 2.055555556) equal to 0.474666877 and -0.474666877.Subproblem 1
x + 2.055555556 = 0.474666877 Simplifying x + 2.055555556 = 0.474666877 Reorder the terms: 2.055555556 + x = 0.474666877 Solving 2.055555556 + x = 0.474666877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.055555556' to each side of the equation. 2.055555556 + -2.055555556 + x = 0.474666877 + -2.055555556 Combine like terms: 2.055555556 + -2.055555556 = 0.000000000 0.000000000 + x = 0.474666877 + -2.055555556 x = 0.474666877 + -2.055555556 Combine like terms: 0.474666877 + -2.055555556 = -1.580888679 x = -1.580888679 Simplifying x = -1.580888679Subproblem 2
x + 2.055555556 = -0.474666877 Simplifying x + 2.055555556 = -0.474666877 Reorder the terms: 2.055555556 + x = -0.474666877 Solving 2.055555556 + x = -0.474666877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.055555556' to each side of the equation. 2.055555556 + -2.055555556 + x = -0.474666877 + -2.055555556 Combine like terms: 2.055555556 + -2.055555556 = 0.000000000 0.000000000 + x = -0.474666877 + -2.055555556 x = -0.474666877 + -2.055555556 Combine like terms: -0.474666877 + -2.055555556 = -2.530222433 x = -2.530222433 Simplifying x = -2.530222433Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.580888679, -2.530222433}
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