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Simplifying 0 = -0.025(x + -80)(x + -80) + 164 Reorder the terms: 0 = -0.025(-80 + x)(x + -80) + 164 Reorder the terms: 0 = -0.025(-80 + x)(-80 + x) + 164 Multiply (-80 + x) * (-80 + x) 0 = -0.025(-80(-80 + x) + x(-80 + x)) + 164 0 = -0.025((-80 * -80 + x * -80) + x(-80 + x)) + 164 0 = -0.025((6400 + -80x) + x(-80 + x)) + 164 0 = -0.025(6400 + -80x + (-80 * x + x * x)) + 164 0 = -0.025(6400 + -80x + (-80x + x2)) + 164 Combine like terms: -80x + -80x = -160x 0 = -0.025(6400 + -160x + x2) + 164 0 = (6400 * -0.025 + -160x * -0.025 + x2 * -0.025) + 164 0 = (-160 + 4x + -0.025x2) + 164 Reorder the terms: 0 = -160 + 164 + 4x + -0.025x2 Combine like terms: -160 + 164 = 4 0 = 4 + 4x + -0.025x2 Solving 0 = 4 + 4x + -0.025x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -4x + 0.025x2 = 4 + 4x + -0.025x2 + -4 + -4x + 0.025x2 Reorder the terms: -4 + -4x + 0.025x2 = 4 + -4 + 4x + -4x + -0.025x2 + 0.025x2 Combine like terms: 4 + -4 = 0 -4 + -4x + 0.025x2 = 0 + 4x + -4x + -0.025x2 + 0.025x2 -4 + -4x + 0.025x2 = 4x + -4x + -0.025x2 + 0.025x2 Combine like terms: 4x + -4x = 0 -4 + -4x + 0.025x2 = 0 + -0.025x2 + 0.025x2 -4 + -4x + 0.025x2 = -0.025x2 + 0.025x2 Combine like terms: -0.025x2 + 0.025x2 = 0.000 -4 + -4x + 0.025x2 = 0.000 Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. -160 + -160x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + -160x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -160x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -160x + x2 = 0 + 160 -160x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -160x + x2 = 160 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = 160 + 6400 Reorder the terms: 6400 + -160x + x2 = 160 + 6400 Combine like terms: 160 + 6400 = 6560 6400 + -160x + x2 = 6560 Factor a perfect square on the left side: (x + -80)(x + -80) = 6560 Calculate the square root of the right side: 80.993826925 Break this problem into two subproblems by setting (x + -80) equal to 80.993826925 and -80.993826925.Subproblem 1
x + -80 = 80.993826925 Simplifying x + -80 = 80.993826925 Reorder the terms: -80 + x = 80.993826925 Solving -80 + x = 80.993826925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 80.993826925 + 80 Combine like terms: -80 + 80 = 0 0 + x = 80.993826925 + 80 x = 80.993826925 + 80 Combine like terms: 80.993826925 + 80 = 160.993826925 x = 160.993826925 Simplifying x = 160.993826925Subproblem 2
x + -80 = -80.993826925 Simplifying x + -80 = -80.993826925 Reorder the terms: -80 + x = -80.993826925 Solving -80 + x = -80.993826925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -80.993826925 + 80 Combine like terms: -80 + 80 = 0 0 + x = -80.993826925 + 80 x = -80.993826925 + 80 Combine like terms: -80.993826925 + 80 = -0.993826925 x = -0.993826925 Simplifying x = -0.993826925Solution
The solution to the problem is based on the solutions from the subproblems. x = {160.993826925, -0.993826925}
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