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Simplifying x2 + 9x + -74 = 0 Reorder the terms: -74 + 9x + x2 = 0 Solving -74 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 9x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + 9x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 9x + x2 = 0 + 74 9x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 9x + x2 = 74 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 74 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 74 + 20.25 Combine like terms: 74 + 20.25 = 94.25 20.25 + 9x + x2 = 94.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + 4.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + 4.5 = 9.708243919 Simplifying x + 4.5 = 9.708243919 Reorder the terms: 4.5 + x = 9.708243919 Solving 4.5 + x = 9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 9.708243919 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 9.708243919 + -4.5 x = 9.708243919 + -4.5 Combine like terms: 9.708243919 + -4.5 = 5.208243919 x = 5.208243919 Simplifying x = 5.208243919Subproblem 2
x + 4.5 = -9.708243919 Simplifying x + 4.5 = -9.708243919 Reorder the terms: 4.5 + x = -9.708243919 Solving 4.5 + x = -9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -9.708243919 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -9.708243919 + -4.5 x = -9.708243919 + -4.5 Combine like terms: -9.708243919 + -4.5 = -14.208243919 x = -14.208243919 Simplifying x = -14.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.208243919, -14.208243919}
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