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Simplifying x2 + 9x + -1608 = 0 Reorder the terms: -1608 + 9x + x2 = 0 Solving -1608 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1608' to each side of the equation. -1608 + 9x + 1608 + x2 = 0 + 1608 Reorder the terms: -1608 + 1608 + 9x + x2 = 0 + 1608 Combine like terms: -1608 + 1608 = 0 0 + 9x + x2 = 0 + 1608 9x + x2 = 0 + 1608 Combine like terms: 0 + 1608 = 1608 9x + x2 = 1608 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 = 1608 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 1608 + 20.25 Combine like terms: 1608 + 20.25 = 1628.25 20.25 + 9x + x2 = 1628.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 1628.25 Calculate the square root of the right side: 40.351579895 Break this problem into two subproblems by setting (x + 4.5) equal to 40.351579895 and -40.351579895.Subproblem 1
x + 4.5 = 40.351579895 Simplifying x + 4.5 = 40.351579895 Reorder the terms: 4.5 + x = 40.351579895 Solving 4.5 + x = 40.351579895 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 = 40.351579895 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 40.351579895 + -4.5 x = 40.351579895 + -4.5 Combine like terms: 40.351579895 + -4.5 = 35.851579895 x = 35.851579895 Simplifying x = 35.851579895Subproblem 2
x + 4.5 = -40.351579895 Simplifying x + 4.5 = -40.351579895 Reorder the terms: 4.5 + x = -40.351579895 Solving 4.5 + x = -40.351579895 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 = -40.351579895 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -40.351579895 + -4.5 x = -40.351579895 + -4.5 Combine like terms: -40.351579895 + -4.5 = -44.851579895 x = -44.851579895 Simplifying x = -44.851579895Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.851579895, -44.851579895}
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