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Simplifying x2 + 56x + 768 = 285 Reorder the terms: 768 + 56x + x2 = 285 Solving 768 + 56x + x2 = 285 Solving for variable 'x'. Reorder the terms: 768 + -285 + 56x + x2 = 285 + -285 Combine like terms: 768 + -285 = 483 483 + 56x + x2 = 285 + -285 Combine like terms: 285 + -285 = 0 483 + 56x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-483' to each side of the equation. 483 + 56x + -483 + x2 = 0 + -483 Reorder the terms: 483 + -483 + 56x + x2 = 0 + -483 Combine like terms: 483 + -483 = 0 0 + 56x + x2 = 0 + -483 56x + x2 = 0 + -483 Combine like terms: 0 + -483 = -483 56x + x2 = -483 The x term is 56x. Take half its coefficient (28). Square it (784) and add it to both sides. Add '784' to each side of the equation. 56x + 784 + x2 = -483 + 784 Reorder the terms: 784 + 56x + x2 = -483 + 784 Combine like terms: -483 + 784 = 301 784 + 56x + x2 = 301 Factor a perfect square on the left side: (x + 28)(x + 28) = 301 Calculate the square root of the right side: 17.349351573 Break this problem into two subproblems by setting (x + 28) equal to 17.349351573 and -17.349351573.Subproblem 1
x + 28 = 17.349351573 Simplifying x + 28 = 17.349351573 Reorder the terms: 28 + x = 17.349351573 Solving 28 + x = 17.349351573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = 17.349351573 + -28 Combine like terms: 28 + -28 = 0 0 + x = 17.349351573 + -28 x = 17.349351573 + -28 Combine like terms: 17.349351573 + -28 = -10.650648427 x = -10.650648427 Simplifying x = -10.650648427Subproblem 2
x + 28 = -17.349351573 Simplifying x + 28 = -17.349351573 Reorder the terms: 28 + x = -17.349351573 Solving 28 + x = -17.349351573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = -17.349351573 + -28 Combine like terms: 28 + -28 = 0 0 + x = -17.349351573 + -28 x = -17.349351573 + -28 Combine like terms: -17.349351573 + -28 = -45.349351573 x = -45.349351573 Simplifying x = -45.349351573Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.650648427, -45.349351573}
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