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Simplifying 0.5x2 + 28x + -369 = 0 Reorder the terms: -369 + 28x + 0.5x2 = 0 Solving -369 + 28x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -738 + 56x + x2 = 0 Move the constant term to the right: Add '738' to each side of the equation. -738 + 56x + 738 + x2 = 0 + 738 Reorder the terms: -738 + 738 + 56x + x2 = 0 + 738 Combine like terms: -738 + 738 = 0 0 + 56x + x2 = 0 + 738 56x + x2 = 0 + 738 Combine like terms: 0 + 738 = 738 56x + x2 = 738 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 = 738 + 784 Reorder the terms: 784 + 56x + x2 = 738 + 784 Combine like terms: 738 + 784 = 1522 784 + 56x + x2 = 1522 Factor a perfect square on the left side: (x + 28)(x + 28) = 1522 Calculate the square root of the right side: 39.012818406 Break this problem into two subproblems by setting (x + 28) equal to 39.012818406 and -39.012818406.Subproblem 1
x + 28 = 39.012818406 Simplifying x + 28 = 39.012818406 Reorder the terms: 28 + x = 39.012818406 Solving 28 + x = 39.012818406 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 = 39.012818406 + -28 Combine like terms: 28 + -28 = 0 0 + x = 39.012818406 + -28 x = 39.012818406 + -28 Combine like terms: 39.012818406 + -28 = 11.012818406 x = 11.012818406 Simplifying x = 11.012818406Subproblem 2
x + 28 = -39.012818406 Simplifying x + 28 = -39.012818406 Reorder the terms: 28 + x = -39.012818406 Solving 28 + x = -39.012818406 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 = -39.012818406 + -28 Combine like terms: 28 + -28 = 0 0 + x = -39.012818406 + -28 x = -39.012818406 + -28 Combine like terms: -39.012818406 + -28 = -67.012818406 x = -67.012818406 Simplifying x = -67.012818406Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.012818406, -67.012818406}
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