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Simplifying x2 + 4x + -10077696 = 0 Reorder the terms: -10077696 + 4x + x2 = 0 Solving -10077696 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10077696' to each side of the equation. -10077696 + 4x + 10077696 + x2 = 0 + 10077696 Reorder the terms: -10077696 + 10077696 + 4x + x2 = 0 + 10077696 Combine like terms: -10077696 + 10077696 = 0 0 + 4x + x2 = 0 + 10077696 4x + x2 = 0 + 10077696 Combine like terms: 0 + 10077696 = 10077696 4x + x2 = 10077696 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 10077696 + 4 Reorder the terms: 4 + 4x + x2 = 10077696 + 4 Combine like terms: 10077696 + 4 = 10077700 4 + 4x + x2 = 10077700 Factor a perfect square on the left side: (x + 2)(x + 2) = 10077700 Calculate the square root of the right side: 3174.53933666 Break this problem into two subproblems by setting (x + 2) equal to 3174.53933666 and -3174.53933666.Subproblem 1
x + 2 = 3174.53933666 Simplifying x + 2 = 3174.53933666 Reorder the terms: 2 + x = 3174.53933666 Solving 2 + x = 3174.53933666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3174.53933666 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3174.53933666 + -2 x = 3174.53933666 + -2 Combine like terms: 3174.53933666 + -2 = 3172.53933666 x = 3172.53933666 Simplifying x = 3172.53933666Subproblem 2
x + 2 = -3174.53933666 Simplifying x + 2 = -3174.53933666 Reorder the terms: 2 + x = -3174.53933666 Solving 2 + x = -3174.53933666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3174.53933666 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3174.53933666 + -2 x = -3174.53933666 + -2 Combine like terms: -3174.53933666 + -2 = -3176.53933666 x = -3176.53933666 Simplifying x = -3176.53933666Solution
The solution to the problem is based on the solutions from the subproblems. x = {3172.53933666, -3176.53933666}
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