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Simplifying 5x2 + -36x + -144 = 0 Reorder the terms: -144 + -36x + 5x2 = 0 Solving -144 + -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'. -28.8 + -7.2x + x2 = 0 Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + -7.2x + 28.8 + x2 = 0 + 28.8 Reorder the terms: -28.8 + 28.8 + -7.2x + x2 = 0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + -7.2x + x2 = 0 + 28.8 -7.2x + x2 = 0 + 28.8 Combine like terms: 0 + 28.8 = 28.8 -7.2x + x2 = 28.8 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 = 28.8 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 28.8 + 12.96 Combine like terms: 28.8 + 12.96 = 41.76 12.96 + -7.2x + x2 = 41.76 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 41.76 Calculate the square root of the right side: 6.462197769 Break this problem into two subproblems by setting (x + -3.6) equal to 6.462197769 and -6.462197769.Subproblem 1
x + -3.6 = 6.462197769 Simplifying x + -3.6 = 6.462197769 Reorder the terms: -3.6 + x = 6.462197769 Solving -3.6 + x = 6.462197769 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 = 6.462197769 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 6.462197769 + 3.6 x = 6.462197769 + 3.6 Combine like terms: 6.462197769 + 3.6 = 10.062197769 x = 10.062197769 Simplifying x = 10.062197769Subproblem 2
x + -3.6 = -6.462197769 Simplifying x + -3.6 = -6.462197769 Reorder the terms: -3.6 + x = -6.462197769 Solving -3.6 + x = -6.462197769 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 = -6.462197769 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -6.462197769 + 3.6 x = -6.462197769 + 3.6 Combine like terms: -6.462197769 + 3.6 = -2.862197769 x = -2.862197769 Simplifying x = -2.862197769Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.062197769, -2.862197769}
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