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Simplifying x = x2 + -9x + -80 Reorder the terms: x = -80 + -9x + x2 Solving x = -80 + -9x + x2 Solving for variable 'x'. Reorder the terms: 80 + x + 9x + -1x2 = -80 + -9x + x2 + 80 + 9x + -1x2 Combine like terms: x + 9x = 10x 80 + 10x + -1x2 = -80 + -9x + x2 + 80 + 9x + -1x2 Reorder the terms: 80 + 10x + -1x2 = -80 + 80 + -9x + 9x + x2 + -1x2 Combine like terms: -80 + 80 = 0 80 + 10x + -1x2 = 0 + -9x + 9x + x2 + -1x2 80 + 10x + -1x2 = -9x + 9x + x2 + -1x2 Combine like terms: -9x + 9x = 0 80 + 10x + -1x2 = 0 + x2 + -1x2 80 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 80 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + -10x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -10x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -10x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -10x + x2 = 0 + 80 -10x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -10x + x2 = 80 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 = 80 + 25 Reorder the terms: 25 + -10x + x2 = 80 + 25 Combine like terms: 80 + 25 = 105 25 + -10x + x2 = 105 Factor a perfect square on the left side: (x + -5)(x + -5) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + -5) equal to 10.246950766 and -10.246950766.Subproblem 1
x + -5 = 10.246950766 Simplifying x + -5 = 10.246950766 Reorder the terms: -5 + x = 10.246950766 Solving -5 + x = 10.246950766 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 = 10.246950766 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.246950766 + 5 x = 10.246950766 + 5 Combine like terms: 10.246950766 + 5 = 15.246950766 x = 15.246950766 Simplifying x = 15.246950766Subproblem 2
x + -5 = -10.246950766 Simplifying x + -5 = -10.246950766 Reorder the terms: -5 + x = -10.246950766 Solving -5 + x = -10.246950766 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 = -10.246950766 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.246950766 + 5 x = -10.246950766 + 5 Combine like terms: -10.246950766 + 5 = -5.246950766 x = -5.246950766 Simplifying x = -5.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.246950766, -5.246950766}
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