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Simplifying 5x2 + -32x + -252 = 0 Reorder the terms: -252 + -32x + 5x2 = 0 Solving -252 + -32x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -50.4 + -6.4x + x2 = 0 Move the constant term to the right: Add '50.4' to each side of the equation. -50.4 + -6.4x + 50.4 + x2 = 0 + 50.4 Reorder the terms: -50.4 + 50.4 + -6.4x + x2 = 0 + 50.4 Combine like terms: -50.4 + 50.4 = 0.0 0.0 + -6.4x + x2 = 0 + 50.4 -6.4x + x2 = 0 + 50.4 Combine like terms: 0 + 50.4 = 50.4 -6.4x + x2 = 50.4 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = 50.4 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = 50.4 + 10.24 Combine like terms: 50.4 + 10.24 = 60.64 10.24 + -6.4x + x2 = 60.64 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 60.64 Calculate the square root of the right side: 7.787168934 Break this problem into two subproblems by setting (x + -3.2) equal to 7.787168934 and -7.787168934.Subproblem 1
x + -3.2 = 7.787168934 Simplifying x + -3.2 = 7.787168934 Reorder the terms: -3.2 + x = 7.787168934 Solving -3.2 + x = 7.787168934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 7.787168934 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 7.787168934 + 3.2 x = 7.787168934 + 3.2 Combine like terms: 7.787168934 + 3.2 = 10.987168934 x = 10.987168934 Simplifying x = 10.987168934Subproblem 2
x + -3.2 = -7.787168934 Simplifying x + -3.2 = -7.787168934 Reorder the terms: -3.2 + x = -7.787168934 Solving -3.2 + x = -7.787168934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -7.787168934 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -7.787168934 + 3.2 x = -7.787168934 + 3.2 Combine like terms: -7.787168934 + 3.2 = -4.587168934 x = -4.587168934 Simplifying x = -4.587168934Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.987168934, -4.587168934}
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