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Simplifying x2 + 13x = 320 Reorder the terms: 13x + x2 = 320 Solving 13x + x2 = 320 Solving for variable 'x'. Reorder the terms: -320 + 13x + x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -320 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + 13x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 13x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 13x + x2 = 0 + 320 13x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 13x + x2 = 320 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 = 320 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 320 + 42.25 Combine like terms: 320 + 42.25 = 362.25 42.25 + 13x + x2 = 362.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 362.25 Calculate the square root of the right side: 19.032866311 Break this problem into two subproblems by setting (x + 6.5) equal to 19.032866311 and -19.032866311.Subproblem 1
x + 6.5 = 19.032866311 Simplifying x + 6.5 = 19.032866311 Reorder the terms: 6.5 + x = 19.032866311 Solving 6.5 + x = 19.032866311 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 = 19.032866311 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 19.032866311 + -6.5 x = 19.032866311 + -6.5 Combine like terms: 19.032866311 + -6.5 = 12.532866311 x = 12.532866311 Simplifying x = 12.532866311Subproblem 2
x + 6.5 = -19.032866311 Simplifying x + 6.5 = -19.032866311 Reorder the terms: 6.5 + x = -19.032866311 Solving 6.5 + x = -19.032866311 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 = -19.032866311 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -19.032866311 + -6.5 x = -19.032866311 + -6.5 Combine like terms: -19.032866311 + -6.5 = -25.532866311 x = -25.532866311 Simplifying x = -25.532866311Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.532866311, -25.532866311}
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