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Simplifying 5x2 + -52x + 116 = 0 Reorder the terms: 116 + -52x + 5x2 = 0 Solving 116 + -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'. 23.2 + -10.4x + x2 = 0 Move the constant term to the right: Add '-23.2' to each side of the equation. 23.2 + -10.4x + -23.2 + x2 = 0 + -23.2 Reorder the terms: 23.2 + -23.2 + -10.4x + x2 = 0 + -23.2 Combine like terms: 23.2 + -23.2 = 0.0 0.0 + -10.4x + x2 = 0 + -23.2 -10.4x + x2 = 0 + -23.2 Combine like terms: 0 + -23.2 = -23.2 -10.4x + x2 = -23.2 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 = -23.2 + 27.04 Reorder the terms: 27.04 + -10.4x + x2 = -23.2 + 27.04 Combine like terms: -23.2 + 27.04 = 3.84 27.04 + -10.4x + x2 = 3.84 Factor a perfect square on the left side: (x + -5.2)(x + -5.2) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (x + -5.2) equal to 1.959591794 and -1.959591794.Subproblem 1
x + -5.2 = 1.959591794 Simplifying x + -5.2 = 1.959591794 Reorder the terms: -5.2 + x = 1.959591794 Solving -5.2 + x = 1.959591794 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 = 1.959591794 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = 1.959591794 + 5.2 x = 1.959591794 + 5.2 Combine like terms: 1.959591794 + 5.2 = 7.159591794 x = 7.159591794 Simplifying x = 7.159591794Subproblem 2
x + -5.2 = -1.959591794 Simplifying x + -5.2 = -1.959591794 Reorder the terms: -5.2 + x = -1.959591794 Solving -5.2 + x = -1.959591794 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 = -1.959591794 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = -1.959591794 + 5.2 x = -1.959591794 + 5.2 Combine like terms: -1.959591794 + 5.2 = 3.240408206 x = 3.240408206 Simplifying x = 3.240408206Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.159591794, 3.240408206}
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