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Simplifying x2 + -40x + 345 = 0 Reorder the terms: 345 + -40x + x2 = 0 Solving 345 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-345' to each side of the equation. 345 + -40x + -345 + x2 = 0 + -345 Reorder the terms: 345 + -345 + -40x + x2 = 0 + -345 Combine like terms: 345 + -345 = 0 0 + -40x + x2 = 0 + -345 -40x + x2 = 0 + -345 Combine like terms: 0 + -345 = -345 -40x + x2 = -345 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -345 + 400 Reorder the terms: 400 + -40x + x2 = -345 + 400 Combine like terms: -345 + 400 = 55 400 + -40x + x2 = 55 Factor a perfect square on the left side: (x + -20)(x + -20) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -20) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -20 = 7.416198487 Simplifying x + -20 = 7.416198487 Reorder the terms: -20 + x = 7.416198487 Solving -20 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 7.416198487 + 20 Combine like terms: -20 + 20 = 0 0 + x = 7.416198487 + 20 x = 7.416198487 + 20 Combine like terms: 7.416198487 + 20 = 27.416198487 x = 27.416198487 Simplifying x = 27.416198487Subproblem 2
x + -20 = -7.416198487 Simplifying x + -20 = -7.416198487 Reorder the terms: -20 + x = -7.416198487 Solving -20 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -7.416198487 + 20 Combine like terms: -20 + 20 = 0 0 + x = -7.416198487 + 20 x = -7.416198487 + 20 Combine like terms: -7.416198487 + 20 = 12.583801513 x = 12.583801513 Simplifying x = 12.583801513Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.416198487, 12.583801513}
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