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Simplifying 100 = x2 + -11x + 45 Reorder the terms: 100 = 45 + -11x + x2 Solving 100 = 45 + -11x + x2 Solving for variable 'x'. Combine like terms: 100 + -45 = 55 55 + 11x + -1x2 = 45 + -11x + x2 + -45 + 11x + -1x2 Reorder the terms: 55 + 11x + -1x2 = 45 + -45 + -11x + 11x + x2 + -1x2 Combine like terms: 45 + -45 = 0 55 + 11x + -1x2 = 0 + -11x + 11x + x2 + -1x2 55 + 11x + -1x2 = -11x + 11x + x2 + -1x2 Combine like terms: -11x + 11x = 0 55 + 11x + -1x2 = 0 + x2 + -1x2 55 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 55 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -55 + -11x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + -11x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -11x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -11x + x2 = 0 + 55 -11x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -11x + x2 = 55 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 55 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 55 + 30.25 Combine like terms: 55 + 30.25 = 85.25 30.25 + -11x + x2 = 85.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + -5.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + -5.5 = 9.233092656 Simplifying x + -5.5 = 9.233092656 Reorder the terms: -5.5 + x = 9.233092656 Solving -5.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 9.233092656 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 9.233092656 + 5.5 x = 9.233092656 + 5.5 Combine like terms: 9.233092656 + 5.5 = 14.733092656 x = 14.733092656 Simplifying x = 14.733092656Subproblem 2
x + -5.5 = -9.233092656 Simplifying x + -5.5 = -9.233092656 Reorder the terms: -5.5 + x = -9.233092656 Solving -5.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -9.233092656 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -9.233092656 + 5.5 x = -9.233092656 + 5.5 Combine like terms: -9.233092656 + 5.5 = -3.733092656 x = -3.733092656 Simplifying x = -3.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.733092656, -3.733092656}
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