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Simplifying x2 + -56x + 216 = 0 Reorder the terms: 216 + -56x + x2 = 0 Solving 216 + -56x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-216' to each side of the equation. 216 + -56x + -216 + x2 = 0 + -216 Reorder the terms: 216 + -216 + -56x + x2 = 0 + -216 Combine like terms: 216 + -216 = 0 0 + -56x + x2 = 0 + -216 -56x + x2 = 0 + -216 Combine like terms: 0 + -216 = -216 -56x + x2 = -216 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 = -216 + 784 Reorder the terms: 784 + -56x + x2 = -216 + 784 Combine like terms: -216 + 784 = 568 784 + -56x + x2 = 568 Factor a perfect square on the left side: (x + -28)(x + -28) = 568 Calculate the square root of the right side: 23.832750576 Break this problem into two subproblems by setting (x + -28) equal to 23.832750576 and -23.832750576.Subproblem 1
x + -28 = 23.832750576 Simplifying x + -28 = 23.832750576 Reorder the terms: -28 + x = 23.832750576 Solving -28 + x = 23.832750576 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 = 23.832750576 + 28 Combine like terms: -28 + 28 = 0 0 + x = 23.832750576 + 28 x = 23.832750576 + 28 Combine like terms: 23.832750576 + 28 = 51.832750576 x = 51.832750576 Simplifying x = 51.832750576Subproblem 2
x + -28 = -23.832750576 Simplifying x + -28 = -23.832750576 Reorder the terms: -28 + x = -23.832750576 Solving -28 + x = -23.832750576 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 = -23.832750576 + 28 Combine like terms: -28 + 28 = 0 0 + x = -23.832750576 + 28 x = -23.832750576 + 28 Combine like terms: -23.832750576 + 28 = 4.167249424 x = 4.167249424 Simplifying x = 4.167249424Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.832750576, 4.167249424}
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