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Simplifying 5x2 + -24x + -144 = 0 Reorder the terms: -144 + -24x + 5x2 = 0 Solving -144 + -24x + 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 + -4.8x + x2 = 0 Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + -4.8x + 28.8 + x2 = 0 + 28.8 Reorder the terms: -28.8 + 28.8 + -4.8x + x2 = 0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + -4.8x + x2 = 0 + 28.8 -4.8x + x2 = 0 + 28.8 Combine like terms: 0 + 28.8 = 28.8 -4.8x + x2 = 28.8 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = 28.8 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = 28.8 + 5.76 Combine like terms: 28.8 + 5.76 = 34.56 5.76 + -4.8x + x2 = 34.56 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 34.56 Calculate the square root of the right side: 5.878775383 Break this problem into two subproblems by setting (x + -2.4) equal to 5.878775383 and -5.878775383.Subproblem 1
x + -2.4 = 5.878775383 Simplifying x + -2.4 = 5.878775383 Reorder the terms: -2.4 + x = 5.878775383 Solving -2.4 + x = 5.878775383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 5.878775383 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 5.878775383 + 2.4 x = 5.878775383 + 2.4 Combine like terms: 5.878775383 + 2.4 = 8.278775383 x = 8.278775383 Simplifying x = 8.278775383Subproblem 2
x + -2.4 = -5.878775383 Simplifying x + -2.4 = -5.878775383 Reorder the terms: -2.4 + x = -5.878775383 Solving -2.4 + x = -5.878775383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -5.878775383 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -5.878775383 + 2.4 x = -5.878775383 + 2.4 Combine like terms: -5.878775383 + 2.4 = -3.478775383 x = -3.478775383 Simplifying x = -3.478775383Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.278775383, -3.478775383}
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