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Simplifying x2 + 16x + -320 = 0 Reorder the terms: -320 + 16x + x2 = 0 Solving -320 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + 16x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 16x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 16x + x2 = 0 + 320 16x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 16x + x2 = 320 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 320 + 64 Reorder the terms: 64 + 16x + x2 = 320 + 64 Combine like terms: 320 + 64 = 384 64 + 16x + x2 = 384 Factor a perfect square on the left side: (x + 8)(x + 8) = 384 Calculate the square root of the right side: 19.595917942 Break this problem into two subproblems by setting (x + 8) equal to 19.595917942 and -19.595917942.Subproblem 1
x + 8 = 19.595917942 Simplifying x + 8 = 19.595917942 Reorder the terms: 8 + x = 19.595917942 Solving 8 + x = 19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 19.595917942 + -8 Combine like terms: 8 + -8 = 0 0 + x = 19.595917942 + -8 x = 19.595917942 + -8 Combine like terms: 19.595917942 + -8 = 11.595917942 x = 11.595917942 Simplifying x = 11.595917942Subproblem 2
x + 8 = -19.595917942 Simplifying x + 8 = -19.595917942 Reorder the terms: 8 + x = -19.595917942 Solving 8 + x = -19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -19.595917942 + -8 Combine like terms: 8 + -8 = 0 0 + x = -19.595917942 + -8 x = -19.595917942 + -8 Combine like terms: -19.595917942 + -8 = -27.595917942 x = -27.595917942 Simplifying x = -27.595917942Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.595917942, -27.595917942}
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