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Simplifying 5x2 + 24x = 384 Reorder the terms: 24x + 5x2 = 384 Solving 24x + 5x2 = 384 Solving for variable 'x'. Reorder the terms: -384 + 24x + 5x2 = 384 + -384 Combine like terms: 384 + -384 = 0 -384 + 24x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -76.8 + 4.8x + x2 = 0 Move the constant term to the right: Add '76.8' to each side of the equation. -76.8 + 4.8x + 76.8 + x2 = 0 + 76.8 Reorder the terms: -76.8 + 76.8 + 4.8x + x2 = 0 + 76.8 Combine like terms: -76.8 + 76.8 = 0.0 0.0 + 4.8x + x2 = 0 + 76.8 4.8x + x2 = 0 + 76.8 Combine like terms: 0 + 76.8 = 76.8 4.8x + x2 = 76.8 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 = 76.8 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 76.8 + 5.76 Combine like terms: 76.8 + 5.76 = 82.56 5.76 + 4.8x + x2 = 82.56 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 82.56 Calculate the square root of the right side: 9.086253353 Break this problem into two subproblems by setting (x + 2.4) equal to 9.086253353 and -9.086253353.Subproblem 1
x + 2.4 = 9.086253353 Simplifying x + 2.4 = 9.086253353 Reorder the terms: 2.4 + x = 9.086253353 Solving 2.4 + x = 9.086253353 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 = 9.086253353 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 9.086253353 + -2.4 x = 9.086253353 + -2.4 Combine like terms: 9.086253353 + -2.4 = 6.686253353 x = 6.686253353 Simplifying x = 6.686253353Subproblem 2
x + 2.4 = -9.086253353 Simplifying x + 2.4 = -9.086253353 Reorder the terms: 2.4 + x = -9.086253353 Solving 2.4 + x = -9.086253353 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 = -9.086253353 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -9.086253353 + -2.4 x = -9.086253353 + -2.4 Combine like terms: -9.086253353 + -2.4 = -11.486253353 x = -11.486253353 Simplifying x = -11.486253353Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.686253353, -11.486253353}
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