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Simplifying 0 = 5x2 + 10x + -108 Reorder the terms: 0 = -108 + 10x + 5x2 Solving 0 = -108 + 10x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 108 = 108 108 + -10x + -5x2 = -108 + 10x + 5x2 + 108 + -10x + -5x2 Reorder the terms: 108 + -10x + -5x2 = -108 + 108 + 10x + -10x + 5x2 + -5x2 Combine like terms: -108 + 108 = 0 108 + -10x + -5x2 = 0 + 10x + -10x + 5x2 + -5x2 108 + -10x + -5x2 = 10x + -10x + 5x2 + -5x2 Combine like terms: 10x + -10x = 0 108 + -10x + -5x2 = 0 + 5x2 + -5x2 108 + -10x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 108 + -10x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -21.6 + 2x + x2 = 0 Move the constant term to the right: Add '21.6' to each side of the equation. -21.6 + 2x + 21.6 + x2 = 0 + 21.6 Reorder the terms: -21.6 + 21.6 + 2x + x2 = 0 + 21.6 Combine like terms: -21.6 + 21.6 = 0.0 0.0 + 2x + x2 = 0 + 21.6 2x + x2 = 0 + 21.6 Combine like terms: 0 + 21.6 = 21.6 2x + x2 = 21.6 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 21.6 + 1 Reorder the terms: 1 + 2x + x2 = 21.6 + 1 Combine like terms: 21.6 + 1 = 22.6 1 + 2x + x2 = 22.6 Factor a perfect square on the left side: (x + 1)(x + 1) = 22.6 Calculate the square root of the right side: 4.75394573 Break this problem into two subproblems by setting (x + 1) equal to 4.75394573 and -4.75394573.Subproblem 1
x + 1 = 4.75394573 Simplifying x + 1 = 4.75394573 Reorder the terms: 1 + x = 4.75394573 Solving 1 + x = 4.75394573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.75394573 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.75394573 + -1 x = 4.75394573 + -1 Combine like terms: 4.75394573 + -1 = 3.75394573 x = 3.75394573 Simplifying x = 3.75394573Subproblem 2
x + 1 = -4.75394573 Simplifying x + 1 = -4.75394573 Reorder the terms: 1 + x = -4.75394573 Solving 1 + x = -4.75394573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.75394573 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.75394573 + -1 x = -4.75394573 + -1 Combine like terms: -4.75394573 + -1 = -5.75394573 x = -5.75394573 Simplifying x = -5.75394573Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.75394573, -5.75394573}
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