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Simplifying 5x2 + -52x + 32 = 0 Reorder the terms: 32 + -52x + 5x2 = 0 Solving 32 + -52x + 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'. 6.4 + -10.4x + x2 = 0 Move the constant term to the right: Add '-6.4' to each side of the equation. 6.4 + -10.4x + -6.4 + x2 = 0 + -6.4 Reorder the terms: 6.4 + -6.4 + -10.4x + x2 = 0 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + -10.4x + x2 = 0 + -6.4 -10.4x + x2 = 0 + -6.4 Combine like terms: 0 + -6.4 = -6.4 -10.4x + x2 = -6.4 The x term is -10.4x. Take half its coefficient (-5.2). Square it (27.04) and add it to both sides. Add '27.04' to each side of the equation. -10.4x + 27.04 + x2 = -6.4 + 27.04 Reorder the terms: 27.04 + -10.4x + x2 = -6.4 + 27.04 Combine like terms: -6.4 + 27.04 = 20.64 27.04 + -10.4x + x2 = 20.64 Factor a perfect square on the left side: (x + -5.2)(x + -5.2) = 20.64 Calculate the square root of the right side: 4.543126677 Break this problem into two subproblems by setting (x + -5.2) equal to 4.543126677 and -4.543126677.Subproblem 1
x + -5.2 = 4.543126677 Simplifying x + -5.2 = 4.543126677 Reorder the terms: -5.2 + x = 4.543126677 Solving -5.2 + x = 4.543126677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + x = 4.543126677 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = 4.543126677 + 5.2 x = 4.543126677 + 5.2 Combine like terms: 4.543126677 + 5.2 = 9.743126677 x = 9.743126677 Simplifying x = 9.743126677Subproblem 2
x + -5.2 = -4.543126677 Simplifying x + -5.2 = -4.543126677 Reorder the terms: -5.2 + x = -4.543126677 Solving -5.2 + x = -4.543126677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + x = -4.543126677 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = -4.543126677 + 5.2 x = -4.543126677 + 5.2 Combine like terms: -4.543126677 + 5.2 = 0.656873323 x = 0.656873323 Simplifying x = 0.656873323Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.743126677, 0.656873323}
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