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Simplifying 5x2 + -24x + 5 = 0 Reorder the terms: 5 + -24x + 5x2 = 0 Solving 5 + -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'. 1 + -4.8x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4.8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.8x + x2 = 0 + -1 -4.8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.8x + x2 = -1 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 = -1 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = -1 + 5.76 Combine like terms: -1 + 5.76 = 4.76 5.76 + -4.8x + x2 = 4.76 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 4.76 Calculate the square root of the right side: 2.181742423 Break this problem into two subproblems by setting (x + -2.4) equal to 2.181742423 and -2.181742423.Subproblem 1
x + -2.4 = 2.181742423 Simplifying x + -2.4 = 2.181742423 Reorder the terms: -2.4 + x = 2.181742423 Solving -2.4 + x = 2.181742423 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 = 2.181742423 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 2.181742423 + 2.4 x = 2.181742423 + 2.4 Combine like terms: 2.181742423 + 2.4 = 4.581742423 x = 4.581742423 Simplifying x = 4.581742423Subproblem 2
x + -2.4 = -2.181742423 Simplifying x + -2.4 = -2.181742423 Reorder the terms: -2.4 + x = -2.181742423 Solving -2.4 + x = -2.181742423 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 = -2.181742423 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -2.181742423 + 2.4 x = -2.181742423 + 2.4 Combine like terms: -2.181742423 + 2.4 = 0.218257577 x = 0.218257577 Simplifying x = 0.218257577Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.581742423, 0.218257577}
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