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Simplifying 5x2 + -24x + -8 = 0 Reorder the terms: -8 + -24x + 5x2 = 0 Solving -8 + -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'. -1.6 + -4.8x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -4.8x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -4.8x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -4.8x + x2 = 0 + 1.6 -4.8x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -4.8x + x2 = 1.6 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 = 1.6 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = 1.6 + 5.76 Combine like terms: 1.6 + 5.76 = 7.36 5.76 + -4.8x + x2 = 7.36 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 7.36 Calculate the square root of the right side: 2.712931993 Break this problem into two subproblems by setting (x + -2.4) equal to 2.712931993 and -2.712931993.Subproblem 1
x + -2.4 = 2.712931993 Simplifying x + -2.4 = 2.712931993 Reorder the terms: -2.4 + x = 2.712931993 Solving -2.4 + x = 2.712931993 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 = 2.712931993 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 2.712931993 + 2.4 x = 2.712931993 + 2.4 Combine like terms: 2.712931993 + 2.4 = 5.112931993 x = 5.112931993 Simplifying x = 5.112931993Subproblem 2
x + -2.4 = -2.712931993 Simplifying x + -2.4 = -2.712931993 Reorder the terms: -2.4 + x = -2.712931993 Solving -2.4 + x = -2.712931993 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 = -2.712931993 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -2.712931993 + 2.4 x = -2.712931993 + 2.4 Combine like terms: -2.712931993 + 2.4 = -0.312931993 x = -0.312931993 Simplifying x = -0.312931993Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.112931993, -0.312931993}
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