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Simplifying -1x2 + 2x = -50 Reorder the terms: 2x + -1x2 = -50 Solving 2x + -1x2 = -50 Solving for variable 'x'. Reorder the terms: 50 + 2x + -1x2 = -50 + 50 Combine like terms: -50 + 50 = 0 50 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -2x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -2x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -2x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -2x + x2 = 0 + 50 -2x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -2x + x2 = 50 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 = 50 + 1 Reorder the terms: 1 + -2x + x2 = 50 + 1 Combine like terms: 50 + 1 = 51 1 + -2x + x2 = 51 Factor a perfect square on the left side: (x + -1)(x + -1) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -1) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -1 = 7.141428429 Simplifying x + -1 = 7.141428429 Reorder the terms: -1 + x = 7.141428429 Solving -1 + x = 7.141428429 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 = 7.141428429 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.141428429 + 1 x = 7.141428429 + 1 Combine like terms: 7.141428429 + 1 = 8.141428429 x = 8.141428429 Simplifying x = 8.141428429Subproblem 2
x + -1 = -7.141428429 Simplifying x + -1 = -7.141428429 Reorder the terms: -1 + x = -7.141428429 Solving -1 + x = -7.141428429 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 = -7.141428429 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.141428429 + 1 x = -7.141428429 + 1 Combine like terms: -7.141428429 + 1 = -6.141428429 x = -6.141428429 Simplifying x = -6.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.141428429, -6.141428429}
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