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Simplifying 2x2 + -22x + 30 = 5 Reorder the terms: 30 + -22x + 2x2 = 5 Solving 30 + -22x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: 30 + -5 + -22x + 2x2 = 5 + -5 Combine like terms: 30 + -5 = 25 25 + -22x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 25 + -22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -11x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -11x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -11x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -11x + x2 = 0 + -12.5 -11x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -11x + x2 = -12.5 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 = -12.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -12.5 + 30.25 Combine like terms: -12.5 + 30.25 = 17.75 30.25 + -11x + x2 = 17.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (x + -5.5) equal to 4.213074887 and -4.213074887.Subproblem 1
x + -5.5 = 4.213074887 Simplifying x + -5.5 = 4.213074887 Reorder the terms: -5.5 + x = 4.213074887 Solving -5.5 + x = 4.213074887 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 = 4.213074887 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.213074887 + 5.5 x = 4.213074887 + 5.5 Combine like terms: 4.213074887 + 5.5 = 9.713074887 x = 9.713074887 Simplifying x = 9.713074887Subproblem 2
x + -5.5 = -4.213074887 Simplifying x + -5.5 = -4.213074887 Reorder the terms: -5.5 + x = -4.213074887 Solving -5.5 + x = -4.213074887 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 = -4.213074887 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.213074887 + 5.5 x = -4.213074887 + 5.5 Combine like terms: -4.213074887 + 5.5 = 1.286925113 x = 1.286925113 Simplifying x = 1.286925113Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.713074887, 1.286925113}
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