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Simplifying 2x2 + 40x + -345 = 0 Reorder the terms: -345 + 40x + 2x2 = 0 Solving -345 + 40x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -172.5 + 20x + x2 = 0 Move the constant term to the right: Add '172.5' to each side of the equation. -172.5 + 20x + 172.5 + x2 = 0 + 172.5 Reorder the terms: -172.5 + 172.5 + 20x + x2 = 0 + 172.5 Combine like terms: -172.5 + 172.5 = 0.0 0.0 + 20x + x2 = 0 + 172.5 20x + x2 = 0 + 172.5 Combine like terms: 0 + 172.5 = 172.5 20x + x2 = 172.5 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 172.5 + 100 Reorder the terms: 100 + 20x + x2 = 172.5 + 100 Combine like terms: 172.5 + 100 = 272.5 100 + 20x + x2 = 272.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 272.5 Calculate the square root of the right side: 16.507574019 Break this problem into two subproblems by setting (x + 10) equal to 16.507574019 and -16.507574019.Subproblem 1
x + 10 = 16.507574019 Simplifying x + 10 = 16.507574019 Reorder the terms: 10 + x = 16.507574019 Solving 10 + x = 16.507574019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 16.507574019 + -10 Combine like terms: 10 + -10 = 0 0 + x = 16.507574019 + -10 x = 16.507574019 + -10 Combine like terms: 16.507574019 + -10 = 6.507574019 x = 6.507574019 Simplifying x = 6.507574019Subproblem 2
x + 10 = -16.507574019 Simplifying x + 10 = -16.507574019 Reorder the terms: 10 + x = -16.507574019 Solving 10 + x = -16.507574019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -16.507574019 + -10 Combine like terms: 10 + -10 = 0 0 + x = -16.507574019 + -10 x = -16.507574019 + -10 Combine like terms: -16.507574019 + -10 = -26.507574019 x = -26.507574019 Simplifying x = -26.507574019Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.507574019, -26.507574019}
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