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Simplifying 49 = x(x + 4) Reorder the terms: 49 = x(4 + x) 49 = (4 * x + x * x) 49 = (4x + x2) Solving 49 = 4x + x2 Solving for variable 'x'. Reorder the terms: 49 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 49 + -4x + -1x2 = 0 + x2 + -1x2 49 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 49 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 4x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 4x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 4x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 4x + x2 = 0 + 49 4x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 4x + x2 = 49 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 = 49 + 4 Reorder the terms: 4 + 4x + x2 = 49 + 4 Combine like terms: 49 + 4 = 53 4 + 4x + x2 = 53 Factor a perfect square on the left side: (x + 2)(x + 2) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + 2) equal to 7.280109889 and -7.280109889.Subproblem 1
x + 2 = 7.280109889 Simplifying x + 2 = 7.280109889 Reorder the terms: 2 + x = 7.280109889 Solving 2 + x = 7.280109889 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 = 7.280109889 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.280109889 + -2 x = 7.280109889 + -2 Combine like terms: 7.280109889 + -2 = 5.280109889 x = 5.280109889 Simplifying x = 5.280109889Subproblem 2
x + 2 = -7.280109889 Simplifying x + 2 = -7.280109889 Reorder the terms: 2 + x = -7.280109889 Solving 2 + x = -7.280109889 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 = -7.280109889 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.280109889 + -2 x = -7.280109889 + -2 Combine like terms: -7.280109889 + -2 = -9.280109889 x = -9.280109889 Simplifying x = -9.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.280109889, -9.280109889}
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