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Simplifying x2 + 112x + -3008 = 0 Reorder the terms: -3008 + 112x + x2 = 0 Solving -3008 + 112x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3008' to each side of the equation. -3008 + 112x + 3008 + x2 = 0 + 3008 Reorder the terms: -3008 + 3008 + 112x + x2 = 0 + 3008 Combine like terms: -3008 + 3008 = 0 0 + 112x + x2 = 0 + 3008 112x + x2 = 0 + 3008 Combine like terms: 0 + 3008 = 3008 112x + x2 = 3008 The x term is 112x. Take half its coefficient (56). Square it (3136) and add it to both sides. Add '3136' to each side of the equation. 112x + 3136 + x2 = 3008 + 3136 Reorder the terms: 3136 + 112x + x2 = 3008 + 3136 Combine like terms: 3008 + 3136 = 6144 3136 + 112x + x2 = 6144 Factor a perfect square on the left side: (x + 56)(x + 56) = 6144 Calculate the square root of the right side: 78.383671769 Break this problem into two subproblems by setting (x + 56) equal to 78.383671769 and -78.383671769.Subproblem 1
x + 56 = 78.383671769 Simplifying x + 56 = 78.383671769 Reorder the terms: 56 + x = 78.383671769 Solving 56 + x = 78.383671769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-56' to each side of the equation. 56 + -56 + x = 78.383671769 + -56 Combine like terms: 56 + -56 = 0 0 + x = 78.383671769 + -56 x = 78.383671769 + -56 Combine like terms: 78.383671769 + -56 = 22.383671769 x = 22.383671769 Simplifying x = 22.383671769Subproblem 2
x + 56 = -78.383671769 Simplifying x + 56 = -78.383671769 Reorder the terms: 56 + x = -78.383671769 Solving 56 + x = -78.383671769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-56' to each side of the equation. 56 + -56 + x = -78.383671769 + -56 Combine like terms: 56 + -56 = 0 0 + x = -78.383671769 + -56 x = -78.383671769 + -56 Combine like terms: -78.383671769 + -56 = -134.383671769 x = -134.383671769 Simplifying x = -134.383671769Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.383671769, -134.383671769}
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