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Simplifying 2x2 + 2x + -153 = 0 Reorder the terms: -153 + 2x + 2x2 = 0 Solving -153 + 2x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -76.5 + x + x2 = 0 Move the constant term to the right: Add '76.5' to each side of the equation. -76.5 + x + 76.5 + x2 = 0 + 76.5 Reorder the terms: -76.5 + 76.5 + x + x2 = 0 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + x + x2 = 0 + 76.5 x + x2 = 0 + 76.5 Combine like terms: 0 + 76.5 = 76.5 x + x2 = 76.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 76.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 76.5 + 0.25 Combine like terms: 76.5 + 0.25 = 76.75 1.25 + x2 = 76.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 76.75 Calculate the square root of the right side: 8.760707734 Break this problem into two subproblems by setting (x + 0.5) equal to 8.760707734 and -8.760707734.Subproblem 1
x + 0.5 = 8.760707734 Simplifying x + 0.5 = 8.760707734 Reorder the terms: 0.5 + x = 8.760707734 Solving 0.5 + x = 8.760707734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 8.760707734 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.760707734 + -0.5 x = 8.760707734 + -0.5 Combine like terms: 8.760707734 + -0.5 = 8.260707734 x = 8.260707734 Simplifying x = 8.260707734Subproblem 2
x + 0.5 = -8.760707734 Simplifying x + 0.5 = -8.760707734 Reorder the terms: 0.5 + x = -8.760707734 Solving 0.5 + x = -8.760707734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -8.760707734 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.760707734 + -0.5 x = -8.760707734 + -0.5 Combine like terms: -8.760707734 + -0.5 = -9.260707734 x = -9.260707734 Simplifying x = -9.260707734Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.260707734, -9.260707734}
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