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Simplifying 160x + -1(x * x) = 4500 Multiply x * x 160x + -1(x2) = 4500 Solving 160x + -1x2 = 4500 Solving for variable 'x'. Reorder the terms: -4500 + 160x + -1x2 = 4500 + -4500 Combine like terms: 4500 + -4500 = 0 -4500 + 160x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4500 + -160x + x2 = 0 Move the constant term to the right: Add '-4500' to each side of the equation. 4500 + -160x + -4500 + x2 = 0 + -4500 Reorder the terms: 4500 + -4500 + -160x + x2 = 0 + -4500 Combine like terms: 4500 + -4500 = 0 0 + -160x + x2 = 0 + -4500 -160x + x2 = 0 + -4500 Combine like terms: 0 + -4500 = -4500 -160x + x2 = -4500 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 = -4500 + 6400 Reorder the terms: 6400 + -160x + x2 = -4500 + 6400 Combine like terms: -4500 + 6400 = 1900 6400 + -160x + x2 = 1900 Factor a perfect square on the left side: (x + -80)(x + -80) = 1900 Calculate the square root of the right side: 43.588989435 Break this problem into two subproblems by setting (x + -80) equal to 43.588989435 and -43.588989435.Subproblem 1
x + -80 = 43.588989435 Simplifying x + -80 = 43.588989435 Reorder the terms: -80 + x = 43.588989435 Solving -80 + x = 43.588989435 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 = 43.588989435 + 80 Combine like terms: -80 + 80 = 0 0 + x = 43.588989435 + 80 x = 43.588989435 + 80 Combine like terms: 43.588989435 + 80 = 123.588989435 x = 123.588989435 Simplifying x = 123.588989435Subproblem 2
x + -80 = -43.588989435 Simplifying x + -80 = -43.588989435 Reorder the terms: -80 + x = -43.588989435 Solving -80 + x = -43.588989435 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 = -43.588989435 + 80 Combine like terms: -80 + 80 = 0 0 + x = -43.588989435 + 80 x = -43.588989435 + 80 Combine like terms: -43.588989435 + 80 = 36.411010565 x = 36.411010565 Simplifying x = 36.411010565Solution
The solution to the problem is based on the solutions from the subproblems. x = {123.588989435, 36.411010565}
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