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Simplifying 4x + 50 = x2 Reorder the terms: 50 + 4x = x2 Solving 50 + 4x = x2 Solving for variable 'x'. Combine like terms: x2 + -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 = 9.348469228 x = 9.348469228 Simplifying x = 9.348469228Subproblem 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 = -5.348469228 x = -5.348469228 Simplifying x = -5.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.348469228, -5.348469228}
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