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Simplifying x2 + -146x + 160 = 0 Reorder the terms: 160 + -146x + x2 = 0 Solving 160 + -146x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-160' to each side of the equation. 160 + -146x + -160 + x2 = 0 + -160 Reorder the terms: 160 + -160 + -146x + x2 = 0 + -160 Combine like terms: 160 + -160 = 0 0 + -146x + x2 = 0 + -160 -146x + x2 = 0 + -160 Combine like terms: 0 + -160 = -160 -146x + x2 = -160 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 = -160 + 5329 Reorder the terms: 5329 + -146x + x2 = -160 + 5329 Combine like terms: -160 + 5329 = 5169 5329 + -146x + x2 = 5169 Factor a perfect square on the left side: (x + -73)(x + -73) = 5169 Calculate the square root of the right side: 71.895757872 Break this problem into two subproblems by setting (x + -73) equal to 71.895757872 and -71.895757872.Subproblem 1
x + -73 = 71.895757872 Simplifying x + -73 = 71.895757872 Reorder the terms: -73 + x = 71.895757872 Solving -73 + x = 71.895757872 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 = 71.895757872 + 73 Combine like terms: -73 + 73 = 0 0 + x = 71.895757872 + 73 x = 71.895757872 + 73 Combine like terms: 71.895757872 + 73 = 144.895757872 x = 144.895757872 Simplifying x = 144.895757872Subproblem 2
x + -73 = -71.895757872 Simplifying x + -73 = -71.895757872 Reorder the terms: -73 + x = -71.895757872 Solving -73 + x = -71.895757872 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 = -71.895757872 + 73 Combine like terms: -73 + 73 = 0 0 + x = -71.895757872 + 73 x = -71.895757872 + 73 Combine like terms: -71.895757872 + 73 = 1.104242128 x = 1.104242128 Simplifying x = 1.104242128Solution
The solution to the problem is based on the solutions from the subproblems. x = {144.895757872, 1.104242128}
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