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Simplifying x2 + 13x + -280 = 0 Reorder the terms: -280 + 13x + x2 = 0 Solving -280 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '280' to each side of the equation. -280 + 13x + 280 + x2 = 0 + 280 Reorder the terms: -280 + 280 + 13x + x2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + 13x + x2 = 0 + 280 13x + x2 = 0 + 280 Combine like terms: 0 + 280 = 280 13x + x2 = 280 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 280 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 280 + 42.25 Combine like terms: 280 + 42.25 = 322.25 42.25 + 13x + x2 = 322.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 322.25 Calculate the square root of the right side: 17.951323071 Break this problem into two subproblems by setting (x + 6.5) equal to 17.951323071 and -17.951323071.Subproblem 1
x + 6.5 = 17.951323071 Simplifying x + 6.5 = 17.951323071 Reorder the terms: 6.5 + x = 17.951323071 Solving 6.5 + x = 17.951323071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 17.951323071 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 17.951323071 + -6.5 x = 17.951323071 + -6.5 Combine like terms: 17.951323071 + -6.5 = 11.451323071 x = 11.451323071 Simplifying x = 11.451323071Subproblem 2
x + 6.5 = -17.951323071 Simplifying x + 6.5 = -17.951323071 Reorder the terms: 6.5 + x = -17.951323071 Solving 6.5 + x = -17.951323071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -17.951323071 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -17.951323071 + -6.5 x = -17.951323071 + -6.5 Combine like terms: -17.951323071 + -6.5 = -24.451323071 x = -24.451323071 Simplifying x = -24.451323071Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.451323071, -24.451323071}
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