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Simplifying 0.5x2 + -11x + 9 = -47 Reorder the terms: 9 + -11x + 0.5x2 = -47 Solving 9 + -11x + 0.5x2 = -47 Solving for variable 'x'. Reorder the terms: 9 + 47 + -11x + 0.5x2 = -47 + 47 Combine like terms: 9 + 47 = 56 56 + -11x + 0.5x2 = -47 + 47 Combine like terms: -47 + 47 = 0 56 + -11x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 112 + -22x + x2 = 0 Move the constant term to the right: Add '-112' to each side of the equation. 112 + -22x + -112 + x2 = 0 + -112 Reorder the terms: 112 + -112 + -22x + x2 = 0 + -112 Combine like terms: 112 + -112 = 0 0 + -22x + x2 = 0 + -112 -22x + x2 = 0 + -112 Combine like terms: 0 + -112 = -112 -22x + x2 = -112 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -112 + 121 Reorder the terms: 121 + -22x + x2 = -112 + 121 Combine like terms: -112 + 121 = 9 121 + -22x + x2 = 9 Factor a perfect square on the left side: (x + -11)(x + -11) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -11) equal to 3 and -3.Subproblem 1
x + -11 = 3 Simplifying x + -11 = 3 Reorder the terms: -11 + x = 3 Solving -11 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 3 + 11 Combine like terms: -11 + 11 = 0 0 + x = 3 + 11 x = 3 + 11 Combine like terms: 3 + 11 = 14 x = 14 Simplifying x = 14Subproblem 2
x + -11 = -3 Simplifying x + -11 = -3 Reorder the terms: -11 + x = -3 Solving -11 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -3 + 11 Combine like terms: -11 + 11 = 0 0 + x = -3 + 11 x = -3 + 11 Combine like terms: -3 + 11 = 8 x = 8 Simplifying x = 8Solution
The solution to the problem is based on the solutions from the subproblems. x = {14, 8}
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