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Simplifying 5x2 + -36x + -108 = 0 Reorder the terms: -108 + -36x + 5x2 = 0 Solving -108 + -36x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -21.6 + -7.2x + x2 = 0 Move the constant term to the right: Add '21.6' to each side of the equation. -21.6 + -7.2x + 21.6 + x2 = 0 + 21.6 Reorder the terms: -21.6 + 21.6 + -7.2x + x2 = 0 + 21.6 Combine like terms: -21.6 + 21.6 = 0.0 0.0 + -7.2x + x2 = 0 + 21.6 -7.2x + x2 = 0 + 21.6 Combine like terms: 0 + 21.6 = 21.6 -7.2x + x2 = 21.6 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = 21.6 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 21.6 + 12.96 Combine like terms: 21.6 + 12.96 = 34.56 12.96 + -7.2x + x2 = 34.56 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 34.56 Calculate the square root of the right side: 5.878775383 Break this problem into two subproblems by setting (x + -3.6) equal to 5.878775383 and -5.878775383.Subproblem 1
x + -3.6 = 5.878775383 Simplifying x + -3.6 = 5.878775383 Reorder the terms: -3.6 + x = 5.878775383 Solving -3.6 + x = 5.878775383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 5.878775383 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 5.878775383 + 3.6 x = 5.878775383 + 3.6 Combine like terms: 5.878775383 + 3.6 = 9.478775383 x = 9.478775383 Simplifying x = 9.478775383Subproblem 2
x + -3.6 = -5.878775383 Simplifying x + -3.6 = -5.878775383 Reorder the terms: -3.6 + x = -5.878775383 Solving -3.6 + x = -5.878775383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -5.878775383 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -5.878775383 + 3.6 x = -5.878775383 + 3.6 Combine like terms: -5.878775383 + 3.6 = -2.278775383 x = -2.278775383 Simplifying x = -2.278775383Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.478775383, -2.278775383}
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