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Simplifying 4x2 + 140x + 621 = 0 Reorder the terms: 621 + 140x + 4x2 = 0 Solving 621 + 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'. 155.25 + 35x + x2 = 0 Move the constant term to the right: Add '-155.25' to each side of the equation. 155.25 + 35x + -155.25 + x2 = 0 + -155.25 Reorder the terms: 155.25 + -155.25 + 35x + x2 = 0 + -155.25 Combine like terms: 155.25 + -155.25 = 0.00 0.00 + 35x + x2 = 0 + -155.25 35x + x2 = 0 + -155.25 Combine like terms: 0 + -155.25 = -155.25 35x + x2 = -155.25 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 = -155.25 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -155.25 + 306.25 Combine like terms: -155.25 + 306.25 = 151 306.25 + 35x + x2 = 151 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + 17.5) equal to 12.288205727 and -12.288205727.Subproblem 1
x + 17.5 = 12.288205727 Simplifying x + 17.5 = 12.288205727 Reorder the terms: 17.5 + x = 12.288205727 Solving 17.5 + x = 12.288205727 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 = 12.288205727 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 12.288205727 + -17.5 x = 12.288205727 + -17.5 Combine like terms: 12.288205727 + -17.5 = -5.211794273 x = -5.211794273 Simplifying x = -5.211794273Subproblem 2
x + 17.5 = -12.288205727 Simplifying x + 17.5 = -12.288205727 Reorder the terms: 17.5 + x = -12.288205727 Solving 17.5 + x = -12.288205727 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 = -12.288205727 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -12.288205727 + -17.5 x = -12.288205727 + -17.5 Combine like terms: -12.288205727 + -17.5 = -29.788205727 x = -29.788205727 Simplifying x = -29.788205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.211794273, -29.788205727}
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