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Simplifying x(x + 9) = 35 Reorder the terms: x(9 + x) = 35 (9 * x + x * x) = 35 (9x + x2) = 35 Solving 9x + x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 9x + x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 9x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 9x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 9x + x2 = 0 + 35 9x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 9x + x2 = 35 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 = 35 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 35 + 20.25 Combine like terms: 35 + 20.25 = 55.25 20.25 + 9x + x2 = 55.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + 4.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + 4.5 = 7.433034374 Simplifying x + 4.5 = 7.433034374 Reorder the terms: 4.5 + x = 7.433034374 Solving 4.5 + x = 7.433034374 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 = 7.433034374 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.433034374 + -4.5 x = 7.433034374 + -4.5 Combine like terms: 7.433034374 + -4.5 = 2.933034374 x = 2.933034374 Simplifying x = 2.933034374Subproblem 2
x + 4.5 = -7.433034374 Simplifying x + 4.5 = -7.433034374 Reorder the terms: 4.5 + x = -7.433034374 Solving 4.5 + x = -7.433034374 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 = -7.433034374 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.433034374 + -4.5 x = -7.433034374 + -4.5 Combine like terms: -7.433034374 + -4.5 = -11.933034374 x = -11.933034374 Simplifying x = -11.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.933034374, -11.933034374}
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