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Simplifying 9x + x2 = 144 Solving 9x + x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 9x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 9x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 9x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 9x + x2 = 0 + 144 9x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 9x + x2 = 144 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 = 144 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 144 + 20.25 Combine like terms: 144 + 20.25 = 164.25 20.25 + 9x + x2 = 164.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 164.25 Calculate the square root of the right side: 12.816005618 Break this problem into two subproblems by setting (x + 4.5) equal to 12.816005618 and -12.816005618.Subproblem 1
x + 4.5 = 12.816005618 Simplifying x + 4.5 = 12.816005618 Reorder the terms: 4.5 + x = 12.816005618 Solving 4.5 + x = 12.816005618 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 = 12.816005618 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 12.816005618 + -4.5 x = 12.816005618 + -4.5 Combine like terms: 12.816005618 + -4.5 = 8.316005618 x = 8.316005618 Simplifying x = 8.316005618Subproblem 2
x + 4.5 = -12.816005618 Simplifying x + 4.5 = -12.816005618 Reorder the terms: 4.5 + x = -12.816005618 Solving 4.5 + x = -12.816005618 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 = -12.816005618 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -12.816005618 + -4.5 x = -12.816005618 + -4.5 Combine like terms: -12.816005618 + -4.5 = -17.316005618 x = -17.316005618 Simplifying x = -17.316005618Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.316005618, -17.316005618}
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