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Simplifying 2x2 = -8x + 45 Reorder the terms: 2x2 = 45 + -8x Solving 2x2 = 45 + -8x Solving for variable 'x'. Reorder the terms: -45 + 8x + 2x2 = 45 + -8x + -45 + 8x Reorder the terms: -45 + 8x + 2x2 = 45 + -45 + -8x + 8x Combine like terms: 45 + -45 = 0 -45 + 8x + 2x2 = 0 + -8x + 8x -45 + 8x + 2x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -45 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 4x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 4x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 4x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 4x + x2 = 0 + 22.5 4x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 4x + x2 = 22.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 22.5 + 4 Reorder the terms: 4 + 4x + x2 = 22.5 + 4 Combine like terms: 22.5 + 4 = 26.5 4 + 4x + x2 = 26.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (x + 2) equal to 5.14781507 and -5.14781507.Subproblem 1
x + 2 = 5.14781507 Simplifying x + 2 = 5.14781507 Reorder the terms: 2 + x = 5.14781507 Solving 2 + x = 5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.14781507 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.14781507 + -2 x = 5.14781507 + -2 Combine like terms: 5.14781507 + -2 = 3.14781507 x = 3.14781507 Simplifying x = 3.14781507Subproblem 2
x + 2 = -5.14781507 Simplifying x + 2 = -5.14781507 Reorder the terms: 2 + x = -5.14781507 Solving 2 + x = -5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.14781507 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.14781507 + -2 x = -5.14781507 + -2 Combine like terms: -5.14781507 + -2 = -7.14781507 x = -7.14781507 Simplifying x = -7.14781507Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.14781507, -7.14781507}
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