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Simplifying (x) = 1x2 + 5x + -50 x = 1x2 + 5x + -50 Reorder the terms: x = -50 + 5x + 1x2 Solving x = -50 + 5x + 1x2 Solving for variable 'x'. Reorder the terms: 50 + x + -5x + -1x2 = -50 + 5x + 1x2 + 50 + -5x + -1x2 Combine like terms: x + -5x = -4x 50 + -4x + -1x2 = -50 + 5x + 1x2 + 50 + -5x + -1x2 Reorder the terms: 50 + -4x + -1x2 = -50 + 50 + 5x + -5x + 1x2 + -1x2 Combine like terms: -50 + 50 = 0 50 + -4x + -1x2 = 0 + 5x + -5x + 1x2 + -1x2 50 + -4x + -1x2 = 5x + -5x + 1x2 + -1x2 Combine like terms: 5x + -5x = 0 50 + -4x + -1x2 = 0 + 1x2 + -1x2 50 + -4x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 50 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + 4x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 4x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 4x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 4x + x2 = 0 + 50 4x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 4x + x2 = 50 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 = 50 + 4 Reorder the terms: 4 + 4x + x2 = 50 + 4 Combine like terms: 50 + 4 = 54 4 + 4x + x2 = 54 Factor a perfect square on the left side: (x + 2)(x + 2) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + 2) equal to 7.348469228 and -7.348469228.Subproblem 1
x + 2 = 7.348469228 Simplifying x + 2 = 7.348469228 Reorder the terms: 2 + x = 7.348469228 Solving 2 + x = 7.348469228 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 = 7.348469228 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.348469228 + -2 x = 7.348469228 + -2 Combine like terms: 7.348469228 + -2 = 5.348469228 x = 5.348469228 Simplifying x = 5.348469228Subproblem 2
x + 2 = -7.348469228 Simplifying x + 2 = -7.348469228 Reorder the terms: 2 + x = -7.348469228 Solving 2 + x = -7.348469228 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 = -7.348469228 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.348469228 + -2 x = -7.348469228 + -2 Combine like terms: -7.348469228 + -2 = -9.348469228 x = -9.348469228 Simplifying x = -9.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.348469228, -9.348469228}
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