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Simplifying x2 + -146x + 1040 = 0 Reorder the terms: 1040 + -146x + x2 = 0 Solving 1040 + -146x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1040' to each side of the equation. 1040 + -146x + -1040 + x2 = 0 + -1040 Reorder the terms: 1040 + -1040 + -146x + x2 = 0 + -1040 Combine like terms: 1040 + -1040 = 0 0 + -146x + x2 = 0 + -1040 -146x + x2 = 0 + -1040 Combine like terms: 0 + -1040 = -1040 -146x + x2 = -1040 The x term is -146x. Take half its coefficient (-73). Square it (5329) and add it to both sides. Add '5329' to each side of the equation. -146x + 5329 + x2 = -1040 + 5329 Reorder the terms: 5329 + -146x + x2 = -1040 + 5329 Combine like terms: -1040 + 5329 = 4289 5329 + -146x + x2 = 4289 Factor a perfect square on the left side: (x + -73)(x + -73) = 4289 Calculate the square root of the right side: 65.49045732 Break this problem into two subproblems by setting (x + -73) equal to 65.49045732 and -65.49045732.Subproblem 1
x + -73 = 65.49045732 Simplifying x + -73 = 65.49045732 Reorder the terms: -73 + x = 65.49045732 Solving -73 + x = 65.49045732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '73' to each side of the equation. -73 + 73 + x = 65.49045732 + 73 Combine like terms: -73 + 73 = 0 0 + x = 65.49045732 + 73 x = 65.49045732 + 73 Combine like terms: 65.49045732 + 73 = 138.49045732 x = 138.49045732 Simplifying x = 138.49045732Subproblem 2
x + -73 = -65.49045732 Simplifying x + -73 = -65.49045732 Reorder the terms: -73 + x = -65.49045732 Solving -73 + x = -65.49045732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '73' to each side of the equation. -73 + 73 + x = -65.49045732 + 73 Combine like terms: -73 + 73 = 0 0 + x = -65.49045732 + 73 x = -65.49045732 + 73 Combine like terms: -65.49045732 + 73 = 7.50954268 x = 7.50954268 Simplifying x = 7.50954268Solution
The solution to the problem is based on the solutions from the subproblems. x = {138.49045732, 7.50954268}
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