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Simplifying 5x2 + 48x + -27 = 5 Reorder the terms: -27 + 48x + 5x2 = 5 Solving -27 + 48x + 5x2 = 5 Solving for variable 'x'. Reorder the terms: -27 + -5 + 48x + 5x2 = 5 + -5 Combine like terms: -27 + -5 = -32 -32 + 48x + 5x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -32 + 48x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.4 + 9.6x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 9.6x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 9.6x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 9.6x + x2 = 0 + 6.4 9.6x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 9.6x + x2 = 6.4 The x term is 9.6x. Take half its coefficient (4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. 9.6x + 23.04 + x2 = 6.4 + 23.04 Reorder the terms: 23.04 + 9.6x + x2 = 6.4 + 23.04 Combine like terms: 6.4 + 23.04 = 29.44 23.04 + 9.6x + x2 = 29.44 Factor a perfect square on the left side: (x + 4.8)(x + 4.8) = 29.44 Calculate the square root of the right side: 5.425863987 Break this problem into two subproblems by setting (x + 4.8) equal to 5.425863987 and -5.425863987.Subproblem 1
x + 4.8 = 5.425863987 Simplifying x + 4.8 = 5.425863987 Reorder the terms: 4.8 + x = 5.425863987 Solving 4.8 + x = 5.425863987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.8' to each side of the equation. 4.8 + -4.8 + x = 5.425863987 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + x = 5.425863987 + -4.8 x = 5.425863987 + -4.8 Combine like terms: 5.425863987 + -4.8 = 0.625863987 x = 0.625863987 Simplifying x = 0.625863987Subproblem 2
x + 4.8 = -5.425863987 Simplifying x + 4.8 = -5.425863987 Reorder the terms: 4.8 + x = -5.425863987 Solving 4.8 + x = -5.425863987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.8' to each side of the equation. 4.8 + -4.8 + x = -5.425863987 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + x = -5.425863987 + -4.8 x = -5.425863987 + -4.8 Combine like terms: -5.425863987 + -4.8 = -10.225863987 x = -10.225863987 Simplifying x = -10.225863987Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.625863987, -10.225863987}
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