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Simplifying x2 + -192x + 660 = 0 Reorder the terms: 660 + -192x + x2 = 0 Solving 660 + -192x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-660' to each side of the equation. 660 + -192x + -660 + x2 = 0 + -660 Reorder the terms: 660 + -660 + -192x + x2 = 0 + -660 Combine like terms: 660 + -660 = 0 0 + -192x + x2 = 0 + -660 -192x + x2 = 0 + -660 Combine like terms: 0 + -660 = -660 -192x + x2 = -660 The x term is -192x. Take half its coefficient (-96). Square it (9216) and add it to both sides. Add '9216' to each side of the equation. -192x + 9216 + x2 = -660 + 9216 Reorder the terms: 9216 + -192x + x2 = -660 + 9216 Combine like terms: -660 + 9216 = 8556 9216 + -192x + x2 = 8556 Factor a perfect square on the left side: (x + -96)(x + -96) = 8556 Calculate the square root of the right side: 92.498648639 Break this problem into two subproblems by setting (x + -96) equal to 92.498648639 and -92.498648639.Subproblem 1
x + -96 = 92.498648639 Simplifying x + -96 = 92.498648639 Reorder the terms: -96 + x = 92.498648639 Solving -96 + x = 92.498648639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '96' to each side of the equation. -96 + 96 + x = 92.498648639 + 96 Combine like terms: -96 + 96 = 0 0 + x = 92.498648639 + 96 x = 92.498648639 + 96 Combine like terms: 92.498648639 + 96 = 188.498648639 x = 188.498648639 Simplifying x = 188.498648639Subproblem 2
x + -96 = -92.498648639 Simplifying x + -96 = -92.498648639 Reorder the terms: -96 + x = -92.498648639 Solving -96 + x = -92.498648639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '96' to each side of the equation. -96 + 96 + x = -92.498648639 + 96 Combine like terms: -96 + 96 = 0 0 + x = -92.498648639 + 96 x = -92.498648639 + 96 Combine like terms: -92.498648639 + 96 = 3.501351361 x = 3.501351361 Simplifying x = 3.501351361Solution
The solution to the problem is based on the solutions from the subproblems. x = {188.498648639, 3.501351361}
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