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Simplifying 5x2 + -55x + 150 = 1 Reorder the terms: 150 + -55x + 5x2 = 1 Solving 150 + -55x + 5x2 = 1 Solving for variable 'x'. Reorder the terms: 150 + -1 + -55x + 5x2 = 1 + -1 Combine like terms: 150 + -1 = 149 149 + -55x + 5x2 = 1 + -1 Combine like terms: 1 + -1 = 0 149 + -55x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 29.8 + -11x + x2 = 0 Move the constant term to the right: Add '-29.8' to each side of the equation. 29.8 + -11x + -29.8 + x2 = 0 + -29.8 Reorder the terms: 29.8 + -29.8 + -11x + x2 = 0 + -29.8 Combine like terms: 29.8 + -29.8 = 0.0 0.0 + -11x + x2 = 0 + -29.8 -11x + x2 = 0 + -29.8 Combine like terms: 0 + -29.8 = -29.8 -11x + x2 = -29.8 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 = -29.8 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -29.8 + 30.25 Combine like terms: -29.8 + 30.25 = 0.45 30.25 + -11x + x2 = 0.45 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (x + -5.5) equal to 0.670820393 and -0.670820393.Subproblem 1
x + -5.5 = 0.670820393 Simplifying x + -5.5 = 0.670820393 Reorder the terms: -5.5 + x = 0.670820393 Solving -5.5 + x = 0.670820393 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 = 0.670820393 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 0.670820393 + 5.5 x = 0.670820393 + 5.5 Combine like terms: 0.670820393 + 5.5 = 6.170820393 x = 6.170820393 Simplifying x = 6.170820393Subproblem 2
x + -5.5 = -0.670820393 Simplifying x + -5.5 = -0.670820393 Reorder the terms: -5.5 + x = -0.670820393 Solving -5.5 + x = -0.670820393 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 = -0.670820393 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -0.670820393 + 5.5 x = -0.670820393 + 5.5 Combine like terms: -0.670820393 + 5.5 = 4.829179607 x = 4.829179607 Simplifying x = 4.829179607Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.170820393, 4.829179607}
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