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Simplifying 300 + -56x + -1x2 = 0 Solving 300 + -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'. -300 + 56x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 56x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 56x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 56x + x2 = 0 + 300 56x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 56x + x2 = 300 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 = 300 + 784 Reorder the terms: 784 + 56x + x2 = 300 + 784 Combine like terms: 300 + 784 = 1084 784 + 56x + x2 = 1084 Factor a perfect square on the left side: (x + 28)(x + 28) = 1084 Calculate the square root of the right side: 32.924155266 Break this problem into two subproblems by setting (x + 28) equal to 32.924155266 and -32.924155266.Subproblem 1
x + 28 = 32.924155266 Simplifying x + 28 = 32.924155266 Reorder the terms: 28 + x = 32.924155266 Solving 28 + x = 32.924155266 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 = 32.924155266 + -28 Combine like terms: 28 + -28 = 0 0 + x = 32.924155266 + -28 x = 32.924155266 + -28 Combine like terms: 32.924155266 + -28 = 4.924155266 x = 4.924155266 Simplifying x = 4.924155266Subproblem 2
x + 28 = -32.924155266 Simplifying x + 28 = -32.924155266 Reorder the terms: 28 + x = -32.924155266 Solving 28 + x = -32.924155266 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 = -32.924155266 + -28 Combine like terms: 28 + -28 = 0 0 + x = -32.924155266 + -28 x = -32.924155266 + -28 Combine like terms: -32.924155266 + -28 = -60.924155266 x = -60.924155266 Simplifying x = -60.924155266Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.924155266, -60.924155266}
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