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Simplifying -1x2 + 56x + 343 = 0 Reorder the terms: 343 + 56x + -1x2 = 0 Solving 343 + 56x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -343 + -56x + x2 = 0 Move the constant term to the right: Add '343' to each side of the equation. -343 + -56x + 343 + x2 = 0 + 343 Reorder the terms: -343 + 343 + -56x + x2 = 0 + 343 Combine like terms: -343 + 343 = 0 0 + -56x + x2 = 0 + 343 -56x + x2 = 0 + 343 Combine like terms: 0 + 343 = 343 -56x + x2 = 343 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 = 343 + 784 Reorder the terms: 784 + -56x + x2 = 343 + 784 Combine like terms: 343 + 784 = 1127 784 + -56x + x2 = 1127 Factor a perfect square on the left side: (x + -28)(x + -28) = 1127 Calculate the square root of the right side: 33.570820663 Break this problem into two subproblems by setting (x + -28) equal to 33.570820663 and -33.570820663.Subproblem 1
x + -28 = 33.570820663 Simplifying x + -28 = 33.570820663 Reorder the terms: -28 + x = 33.570820663 Solving -28 + x = 33.570820663 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 = 33.570820663 + 28 Combine like terms: -28 + 28 = 0 0 + x = 33.570820663 + 28 x = 33.570820663 + 28 Combine like terms: 33.570820663 + 28 = 61.570820663 x = 61.570820663 Simplifying x = 61.570820663Subproblem 2
x + -28 = -33.570820663 Simplifying x + -28 = -33.570820663 Reorder the terms: -28 + x = -33.570820663 Solving -28 + x = -33.570820663 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 = -33.570820663 + 28 Combine like terms: -28 + 28 = 0 0 + x = -33.570820663 + 28 x = -33.570820663 + 28 Combine like terms: -33.570820663 + 28 = -5.570820663 x = -5.570820663 Simplifying x = -5.570820663Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.570820663, -5.570820663}
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