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Simplifying 4x2 + 140x + -257 = 0 Reorder the terms: -257 + 140x + 4x2 = 0 Solving -257 + 140x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -64.25 + 35x + x2 = 0 Move the constant term to the right: Add '64.25' to each side of the equation. -64.25 + 35x + 64.25 + x2 = 0 + 64.25 Reorder the terms: -64.25 + 64.25 + 35x + x2 = 0 + 64.25 Combine like terms: -64.25 + 64.25 = 0.00 0.00 + 35x + x2 = 0 + 64.25 35x + x2 = 0 + 64.25 Combine like terms: 0 + 64.25 = 64.25 35x + x2 = 64.25 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 64.25 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 64.25 + 306.25 Combine like terms: 64.25 + 306.25 = 370.5 306.25 + 35x + x2 = 370.5 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 370.5 Calculate the square root of the right side: 19.248376555 Break this problem into two subproblems by setting (x + 17.5) equal to 19.248376555 and -19.248376555.Subproblem 1
x + 17.5 = 19.248376555 Simplifying x + 17.5 = 19.248376555 Reorder the terms: 17.5 + x = 19.248376555 Solving 17.5 + x = 19.248376555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 19.248376555 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 19.248376555 + -17.5 x = 19.248376555 + -17.5 Combine like terms: 19.248376555 + -17.5 = 1.748376555 x = 1.748376555 Simplifying x = 1.748376555Subproblem 2
x + 17.5 = -19.248376555 Simplifying x + 17.5 = -19.248376555 Reorder the terms: 17.5 + x = -19.248376555 Solving 17.5 + x = -19.248376555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -19.248376555 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -19.248376555 + -17.5 x = -19.248376555 + -17.5 Combine like terms: -19.248376555 + -17.5 = -36.748376555 x = -36.748376555 Simplifying x = -36.748376555Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.748376555, -36.748376555}
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