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Simplifying 5x2 + 24x + -20 = 0 Reorder the terms: -20 + 24x + 5x2 = 0 Solving -20 + 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'. -4 + 4.8x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 4.8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 4.8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4.8x + x2 = 0 + 4 4.8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 4.8x + x2 = 4 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 = 4 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 4 + 5.76 Combine like terms: 4 + 5.76 = 9.76 5.76 + 4.8x + x2 = 9.76 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 9.76 Calculate the square root of the right side: 3.12409987 Break this problem into two subproblems by setting (x + 2.4) equal to 3.12409987 and -3.12409987.Subproblem 1
x + 2.4 = 3.12409987 Simplifying x + 2.4 = 3.12409987 Reorder the terms: 2.4 + x = 3.12409987 Solving 2.4 + x = 3.12409987 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 = 3.12409987 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 3.12409987 + -2.4 x = 3.12409987 + -2.4 Combine like terms: 3.12409987 + -2.4 = 0.72409987 x = 0.72409987 Simplifying x = 0.72409987Subproblem 2
x + 2.4 = -3.12409987 Simplifying x + 2.4 = -3.12409987 Reorder the terms: 2.4 + x = -3.12409987 Solving 2.4 + x = -3.12409987 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 = -3.12409987 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -3.12409987 + -2.4 x = -3.12409987 + -2.4 Combine like terms: -3.12409987 + -2.4 = -5.52409987 x = -5.52409987 Simplifying x = -5.52409987Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.72409987, -5.52409987}
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