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Simplifying 50 = x2 + -8x Reorder the terms: 50 = -8x + x2 Solving 50 = -8x + x2 Solving for variable 'x'. Reorder the terms: 50 + 8x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 50 + 8x + -1x2 = 0 + x2 + -1x2 50 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 50 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -8x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -8x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -8x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -8x + x2 = 0 + 50 -8x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -8x + x2 = 50 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 50 + 16 Reorder the terms: 16 + -8x + x2 = 50 + 16 Combine like terms: 50 + 16 = 66 16 + -8x + x2 = 66 Factor a perfect square on the left side: (x + -4)(x + -4) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + -4) equal to 8.124038405 and -8.124038405.Subproblem 1
x + -4 = 8.124038405 Simplifying x + -4 = 8.124038405 Reorder the terms: -4 + x = 8.124038405 Solving -4 + x = 8.124038405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.124038405 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.124038405 + 4 x = 8.124038405 + 4 Combine like terms: 8.124038405 + 4 = 12.124038405 x = 12.124038405 Simplifying x = 12.124038405Subproblem 2
x + -4 = -8.124038405 Simplifying x + -4 = -8.124038405 Reorder the terms: -4 + x = -8.124038405 Solving -4 + x = -8.124038405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.124038405 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.124038405 + 4 x = -8.124038405 + 4 Combine like terms: -8.124038405 + 4 = -4.124038405 x = -4.124038405 Simplifying x = -4.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.124038405, -4.124038405}
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