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Simplifying 28 + -56x = x2 Solving 28 + -56x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 28 + -56x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + 56x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 56x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 56x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 56x + x2 = 0 + 28 56x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 56x + x2 = 28 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 = 28 + 784 Reorder the terms: 784 + 56x + x2 = 28 + 784 Combine like terms: 28 + 784 = 812 784 + 56x + x2 = 812 Factor a perfect square on the left side: (x + 28)(x + 28) = 812 Calculate the square root of the right side: 28.495613698 Break this problem into two subproblems by setting (x + 28) equal to 28.495613698 and -28.495613698.Subproblem 1
x + 28 = 28.495613698 Simplifying x + 28 = 28.495613698 Reorder the terms: 28 + x = 28.495613698 Solving 28 + x = 28.495613698 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 = 28.495613698 + -28 Combine like terms: 28 + -28 = 0 0 + x = 28.495613698 + -28 x = 28.495613698 + -28 Combine like terms: 28.495613698 + -28 = 0.495613698 x = 0.495613698 Simplifying x = 0.495613698Subproblem 2
x + 28 = -28.495613698 Simplifying x + 28 = -28.495613698 Reorder the terms: 28 + x = -28.495613698 Solving 28 + x = -28.495613698 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 = -28.495613698 + -28 Combine like terms: 28 + -28 = 0 0 + x = -28.495613698 + -28 x = -28.495613698 + -28 Combine like terms: -28.495613698 + -28 = -56.495613698 x = -56.495613698 Simplifying x = -56.495613698Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.495613698, -56.495613698}
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