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Simplifying 36x2 + 180x + -65 = 0 Reorder the terms: -65 + 180x + 36x2 = 0 Solving -65 + 180x + 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'. -1.805555556 + 5x + x2 = 0 Move the constant term to the right: Add '1.805555556' to each side of the equation. -1.805555556 + 5x + 1.805555556 + x2 = 0 + 1.805555556 Reorder the terms: -1.805555556 + 1.805555556 + 5x + x2 = 0 + 1.805555556 Combine like terms: -1.805555556 + 1.805555556 = 0.000000000 0.000000000 + 5x + x2 = 0 + 1.805555556 5x + x2 = 0 + 1.805555556 Combine like terms: 0 + 1.805555556 = 1.805555556 5x + x2 = 1.805555556 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1.805555556 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1.805555556 + 6.25 Combine like terms: 1.805555556 + 6.25 = 8.055555556 6.25 + 5x + x2 = 8.055555556 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 8.055555556 Calculate the square root of the right side: 2.838231061 Break this problem into two subproblems by setting (x + 2.5) equal to 2.838231061 and -2.838231061.Subproblem 1
x + 2.5 = 2.838231061 Simplifying x + 2.5 = 2.838231061 Reorder the terms: 2.5 + x = 2.838231061 Solving 2.5 + x = 2.838231061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.838231061 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.838231061 + -2.5 x = 2.838231061 + -2.5 Combine like terms: 2.838231061 + -2.5 = 0.338231061 x = 0.338231061 Simplifying x = 0.338231061Subproblem 2
x + 2.5 = -2.838231061 Simplifying x + 2.5 = -2.838231061 Reorder the terms: 2.5 + x = -2.838231061 Solving 2.5 + x = -2.838231061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.838231061 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.838231061 + -2.5 x = -2.838231061 + -2.5 Combine like terms: -2.838231061 + -2.5 = -5.338231061 x = -5.338231061 Simplifying x = -5.338231061Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.338231061, -5.338231061}
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