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Simplifying -1x2 + 17x + -24 = 0 Reorder the terms: -24 + 17x + -1x2 = 0 Solving -24 + 17x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -17x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -17x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -17x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -17x + x2 = 0 + -24 -17x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -17x + x2 = -24 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -24 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -24 + 72.25 Combine like terms: -24 + 72.25 = 48.25 72.25 + -17x + x2 = 48.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -8.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -8.5 = 6.946221995 Simplifying x + -8.5 = 6.946221995 Reorder the terms: -8.5 + x = 6.946221995 Solving -8.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 6.946221995 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 6.946221995 + 8.5 x = 6.946221995 + 8.5 Combine like terms: 6.946221995 + 8.5 = 15.446221995 x = 15.446221995 Simplifying x = 15.446221995Subproblem 2
x + -8.5 = -6.946221995 Simplifying x + -8.5 = -6.946221995 Reorder the terms: -8.5 + x = -6.946221995 Solving -8.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -6.946221995 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -6.946221995 + 8.5 x = -6.946221995 + 8.5 Combine like terms: -6.946221995 + 8.5 = 1.553778005 x = 1.553778005 Simplifying x = 1.553778005Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.446221995, 1.553778005}
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