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Simplifying 2x * x + -4x + -51 = 0 Multiply x * x 2x2 + -4x + -51 = 0 Reorder the terms: -51 + -4x + 2x2 = 0 Solving -51 + -4x + 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'. -25.5 + -2x + x2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + -2x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + -2x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + -2x + x2 = 0 + 25.5 -2x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 -2x + x2 = 25.5 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 = 25.5 + 1 Reorder the terms: 1 + -2x + x2 = 25.5 + 1 Combine like terms: 25.5 + 1 = 26.5 1 + -2x + x2 = 26.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (x + -1) equal to 5.14781507 and -5.14781507.Subproblem 1
x + -1 = 5.14781507 Simplifying x + -1 = 5.14781507 Reorder the terms: -1 + x = 5.14781507 Solving -1 + x = 5.14781507 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 = 5.14781507 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.14781507 + 1 x = 5.14781507 + 1 Combine like terms: 5.14781507 + 1 = 6.14781507 x = 6.14781507 Simplifying x = 6.14781507Subproblem 2
x + -1 = -5.14781507 Simplifying x + -1 = -5.14781507 Reorder the terms: -1 + x = -5.14781507 Solving -1 + x = -5.14781507 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 = -5.14781507 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.14781507 + 1 x = -5.14781507 + 1 Combine like terms: -5.14781507 + 1 = -4.14781507 x = -4.14781507 Simplifying x = -4.14781507Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.14781507, -4.14781507}
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