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Simplifying 10x2 + 108.5x + 11 = 0 Reorder the terms: 11 + 108.5x + 10x2 = 0 Solving 11 + 108.5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.1 + 10.85x + x2 = 0 Move the constant term to the right: Add '-1.1' to each side of the equation. 1.1 + 10.85x + -1.1 + x2 = 0 + -1.1 Reorder the terms: 1.1 + -1.1 + 10.85x + x2 = 0 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + 10.85x + x2 = 0 + -1.1 10.85x + x2 = 0 + -1.1 Combine like terms: 0 + -1.1 = -1.1 10.85x + x2 = -1.1 The x term is 10.85x. Take half its coefficient (5.425). Square it (29.430625) and add it to both sides. Add '29.430625' to each side of the equation. 10.85x + 29.430625 + x2 = -1.1 + 29.430625 Reorder the terms: 29.430625 + 10.85x + x2 = -1.1 + 29.430625 Combine like terms: -1.1 + 29.430625 = 28.330625 29.430625 + 10.85x + x2 = 28.330625 Factor a perfect square on the left side: (x + 5.425)(x + 5.425) = 28.330625 Calculate the square root of the right side: 5.322652065 Break this problem into two subproblems by setting (x + 5.425) equal to 5.322652065 and -5.322652065.Subproblem 1
x + 5.425 = 5.322652065 Simplifying x + 5.425 = 5.322652065 Reorder the terms: 5.425 + x = 5.322652065 Solving 5.425 + x = 5.322652065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.425' to each side of the equation. 5.425 + -5.425 + x = 5.322652065 + -5.425 Combine like terms: 5.425 + -5.425 = 0.000 0.000 + x = 5.322652065 + -5.425 x = 5.322652065 + -5.425 Combine like terms: 5.322652065 + -5.425 = -0.102347935 x = -0.102347935 Simplifying x = -0.102347935Subproblem 2
x + 5.425 = -5.322652065 Simplifying x + 5.425 = -5.322652065 Reorder the terms: 5.425 + x = -5.322652065 Solving 5.425 + x = -5.322652065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.425' to each side of the equation. 5.425 + -5.425 + x = -5.322652065 + -5.425 Combine like terms: 5.425 + -5.425 = 0.000 0.000 + x = -5.322652065 + -5.425 x = -5.322652065 + -5.425 Combine like terms: -5.322652065 + -5.425 = -10.747652065 x = -10.747652065 Simplifying x = -10.747652065Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.102347935, -10.747652065}
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