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Simplifying x(x + -4) + (x + 9) = 180 Reorder the terms: x(-4 + x) + (x + 9) = 180 (-4 * x + x * x) + (x + 9) = 180 (-4x + x2) + (x + 9) = 180 Reorder the terms: -4x + x2 + (9 + x) = 180 Remove parenthesis around (9 + x) -4x + x2 + 9 + x = 180 Reorder the terms: 9 + -4x + x + x2 = 180 Combine like terms: -4x + x = -3x 9 + -3x + x2 = 180 Solving 9 + -3x + x2 = 180 Solving for variable 'x'. Reorder the terms: 9 + -180 + -3x + x2 = 180 + -180 Combine like terms: 9 + -180 = -171 -171 + -3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -171 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '171' to each side of the equation. -171 + -3x + 171 + x2 = 0 + 171 Reorder the terms: -171 + 171 + -3x + x2 = 0 + 171 Combine like terms: -171 + 171 = 0 0 + -3x + x2 = 0 + 171 -3x + x2 = 0 + 171 Combine like terms: 0 + 171 = 171 -3x + x2 = 171 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 171 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 171 + 2.25 Combine like terms: 171 + 2.25 = 173.25 2.25 + -3x + x2 = 173.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 173.25 Calculate the square root of the right side: 13.162446581 Break this problem into two subproblems by setting (x + -1.5) equal to 13.162446581 and -13.162446581.Subproblem 1
x + -1.5 = 13.162446581 Simplifying x + -1.5 = 13.162446581 Reorder the terms: -1.5 + x = 13.162446581 Solving -1.5 + x = 13.162446581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 13.162446581 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 13.162446581 + 1.5 x = 13.162446581 + 1.5 Combine like terms: 13.162446581 + 1.5 = 14.662446581 x = 14.662446581 Simplifying x = 14.662446581Subproblem 2
x + -1.5 = -13.162446581 Simplifying x + -1.5 = -13.162446581 Reorder the terms: -1.5 + x = -13.162446581 Solving -1.5 + x = -13.162446581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -13.162446581 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -13.162446581 + 1.5 x = -13.162446581 + 1.5 Combine like terms: -13.162446581 + 1.5 = -11.662446581 x = -11.662446581 Simplifying x = -11.662446581Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.662446581, -11.662446581}
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