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Simplifying 2x2 + 20x + -52 = 3 Reorder the terms: -52 + 20x + 2x2 = 3 Solving -52 + 20x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -52 + -3 + 20x + 2x2 = 3 + -3 Combine like terms: -52 + -3 = -55 -55 + 20x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -55 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27.5 + 10x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 10x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + 10x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 10x + x2 = 0 + 27.5 10x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 10x + x2 = 27.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 27.5 + 25 Reorder the terms: 25 + 10x + x2 = 27.5 + 25 Combine like terms: 27.5 + 25 = 52.5 25 + 10x + x2 = 52.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 52.5 Calculate the square root of the right side: 7.245688373 Break this problem into two subproblems by setting (x + 5) equal to 7.245688373 and -7.245688373.Subproblem 1
x + 5 = 7.245688373 Simplifying x + 5 = 7.245688373 Reorder the terms: 5 + x = 7.245688373 Solving 5 + x = 7.245688373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.245688373 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.245688373 + -5 x = 7.245688373 + -5 Combine like terms: 7.245688373 + -5 = 2.245688373 x = 2.245688373 Simplifying x = 2.245688373Subproblem 2
x + 5 = -7.245688373 Simplifying x + 5 = -7.245688373 Reorder the terms: 5 + x = -7.245688373 Solving 5 + x = -7.245688373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.245688373 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.245688373 + -5 x = -7.245688373 + -5 Combine like terms: -7.245688373 + -5 = -12.245688373 x = -12.245688373 Simplifying x = -12.245688373Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.245688373, -12.245688373}
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