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Simplifying 36x2 + -324x + -679 = 0 Reorder the terms: -679 + -324x + 36x2 = 0 Solving -679 + -324x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -18.86111111 + -9x + x2 = 0 Move the constant term to the right: Add '18.86111111' to each side of the equation. -18.86111111 + -9x + 18.86111111 + x2 = 0 + 18.86111111 Reorder the terms: -18.86111111 + 18.86111111 + -9x + x2 = 0 + 18.86111111 Combine like terms: -18.86111111 + 18.86111111 = 0.00000000 0.00000000 + -9x + x2 = 0 + 18.86111111 -9x + x2 = 0 + 18.86111111 Combine like terms: 0 + 18.86111111 = 18.86111111 -9x + x2 = 18.86111111 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 18.86111111 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 18.86111111 + 20.25 Combine like terms: 18.86111111 + 20.25 = 39.11111111 20.25 + -9x + x2 = 39.11111111 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 39.11111111 Calculate the square root of the right side: 6.25388768 Break this problem into two subproblems by setting (x + -4.5) equal to 6.25388768 and -6.25388768.Subproblem 1
x + -4.5 = 6.25388768 Simplifying x + -4.5 = 6.25388768 Reorder the terms: -4.5 + x = 6.25388768 Solving -4.5 + x = 6.25388768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 6.25388768 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.25388768 + 4.5 x = 6.25388768 + 4.5 Combine like terms: 6.25388768 + 4.5 = 10.75388768 x = 10.75388768 Simplifying x = 10.75388768Subproblem 2
x + -4.5 = -6.25388768 Simplifying x + -4.5 = -6.25388768 Reorder the terms: -4.5 + x = -6.25388768 Solving -4.5 + x = -6.25388768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -6.25388768 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.25388768 + 4.5 x = -6.25388768 + 4.5 Combine like terms: -6.25388768 + 4.5 = -1.75388768 x = -1.75388768 Simplifying x = -1.75388768Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.75388768, -1.75388768}
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