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Simplifying -1x2 + 17x + 45 = 0 Reorder the terms: 45 + 17x + -1x2 = 0 Solving 45 + 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'. -45 + -17x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -17x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -17x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -17x + x2 = 0 + 45 -17x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -17x + x2 = 45 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 = 45 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 45 + 72.25 Combine like terms: 45 + 72.25 = 117.25 72.25 + -17x + x2 = 117.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 117.25 Calculate the square root of the right side: 10.828203914 Break this problem into two subproblems by setting (x + -8.5) equal to 10.828203914 and -10.828203914.Subproblem 1
x + -8.5 = 10.828203914 Simplifying x + -8.5 = 10.828203914 Reorder the terms: -8.5 + x = 10.828203914 Solving -8.5 + x = 10.828203914 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 = 10.828203914 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 10.828203914 + 8.5 x = 10.828203914 + 8.5 Combine like terms: 10.828203914 + 8.5 = 19.328203914 x = 19.328203914 Simplifying x = 19.328203914Subproblem 2
x + -8.5 = -10.828203914 Simplifying x + -8.5 = -10.828203914 Reorder the terms: -8.5 + x = -10.828203914 Solving -8.5 + x = -10.828203914 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 = -10.828203914 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -10.828203914 + 8.5 x = -10.828203914 + 8.5 Combine like terms: -10.828203914 + 8.5 = -2.328203914 x = -2.328203914 Simplifying x = -2.328203914Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.328203914, -2.328203914}
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