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Simplifying 5x2 + -24x + -5 = 5 Reorder the terms: -5 + -24x + 5x2 = 5 Solving -5 + -24x + 5x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -5 + -24x + 5x2 = 5 + -5 Combine like terms: -5 + -5 = -10 -10 + -24x + 5x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -10 + -24x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -4.8x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4.8x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -4.8x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4.8x + x2 = 0 + 2 -4.8x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4.8x + x2 = 2 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 = 2 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = 2 + 5.76 Combine like terms: 2 + 5.76 = 7.76 5.76 + -4.8x + x2 = 7.76 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 7.76 Calculate the square root of the right side: 2.785677655 Break this problem into two subproblems by setting (x + -2.4) equal to 2.785677655 and -2.785677655.Subproblem 1
x + -2.4 = 2.785677655 Simplifying x + -2.4 = 2.785677655 Reorder the terms: -2.4 + x = 2.785677655 Solving -2.4 + x = 2.785677655 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 = 2.785677655 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 2.785677655 + 2.4 x = 2.785677655 + 2.4 Combine like terms: 2.785677655 + 2.4 = 5.185677655 x = 5.185677655 Simplifying x = 5.185677655Subproblem 2
x + -2.4 = -2.785677655 Simplifying x + -2.4 = -2.785677655 Reorder the terms: -2.4 + x = -2.785677655 Solving -2.4 + x = -2.785677655 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 = -2.785677655 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -2.785677655 + 2.4 x = -2.785677655 + 2.4 Combine like terms: -2.785677655 + 2.4 = -0.385677655 x = -0.385677655 Simplifying x = -0.385677655Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.185677655, -0.385677655}
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