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Simplifying -1x2 + 110x + -300 = 0 Reorder the terms: -300 + 110x + -1x2 = 0 Solving -300 + 110x + -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 + -110x + x2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -110x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -110x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -110x + x2 = 0 + -300 -110x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -110x + x2 = -300 The x term is -110x. Take half its coefficient (-55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. -110x + 3025 + x2 = -300 + 3025 Reorder the terms: 3025 + -110x + x2 = -300 + 3025 Combine like terms: -300 + 3025 = 2725 3025 + -110x + x2 = 2725 Factor a perfect square on the left side: (x + -55)(x + -55) = 2725 Calculate the square root of the right side: 52.201532545 Break this problem into two subproblems by setting (x + -55) equal to 52.201532545 and -52.201532545.Subproblem 1
x + -55 = 52.201532545 Simplifying x + -55 = 52.201532545 Reorder the terms: -55 + x = 52.201532545 Solving -55 + x = 52.201532545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = 52.201532545 + 55 Combine like terms: -55 + 55 = 0 0 + x = 52.201532545 + 55 x = 52.201532545 + 55 Combine like terms: 52.201532545 + 55 = 107.201532545 x = 107.201532545 Simplifying x = 107.201532545Subproblem 2
x + -55 = -52.201532545 Simplifying x + -55 = -52.201532545 Reorder the terms: -55 + x = -52.201532545 Solving -55 + x = -52.201532545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = -52.201532545 + 55 Combine like terms: -55 + 55 = 0 0 + x = -52.201532545 + 55 x = -52.201532545 + 55 Combine like terms: -52.201532545 + 55 = 2.798467455 x = 2.798467455 Simplifying x = 2.798467455Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.201532545, 2.798467455}
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