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Simplifying 5x2 + -50x + 116 = 0 Reorder the terms: 116 + -50x + 5x2 = 0 Solving 116 + -50x + 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 + -10x + x2 = 0 Move the constant term to the right: Add '-23.2' to each side of the equation. 23.2 + -10x + -23.2 + x2 = 0 + -23.2 Reorder the terms: 23.2 + -23.2 + -10x + x2 = 0 + -23.2 Combine like terms: 23.2 + -23.2 = 0.0 0.0 + -10x + x2 = 0 + -23.2 -10x + x2 = 0 + -23.2 Combine like terms: 0 + -23.2 = -23.2 -10x + x2 = -23.2 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 = -23.2 + 25 Reorder the terms: 25 + -10x + x2 = -23.2 + 25 Combine like terms: -23.2 + 25 = 1.8 25 + -10x + x2 = 1.8 Factor a perfect square on the left side: (x + -5)(x + -5) = 1.8 Calculate the square root of the right side: 1.341640787 Break this problem into two subproblems by setting (x + -5) equal to 1.341640787 and -1.341640787.Subproblem 1
x + -5 = 1.341640787 Simplifying x + -5 = 1.341640787 Reorder the terms: -5 + x = 1.341640787 Solving -5 + x = 1.341640787 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 = 1.341640787 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.341640787 + 5 x = 1.341640787 + 5 Combine like terms: 1.341640787 + 5 = 6.341640787 x = 6.341640787 Simplifying x = 6.341640787Subproblem 2
x + -5 = -1.341640787 Simplifying x + -5 = -1.341640787 Reorder the terms: -5 + x = -1.341640787 Solving -5 + x = -1.341640787 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 = -1.341640787 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.341640787 + 5 x = -1.341640787 + 5 Combine like terms: -1.341640787 + 5 = 3.658359213 x = 3.658359213 Simplifying x = 3.658359213Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.341640787, 3.658359213}
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