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Simplifying 135 = x2 + 4x Reorder the terms: 135 = 4x + x2 Solving 135 = 4x + x2 Solving for variable 'x'. Reorder the terms: 135 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 135 + -4x + -1x2 = 0 + x2 + -1x2 135 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 135 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -135 + 4x + x2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + 4x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + 4x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 4x + x2 = 0 + 135 4x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 4x + x2 = 135 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 = 135 + 4 Reorder the terms: 4 + 4x + x2 = 135 + 4 Combine like terms: 135 + 4 = 139 4 + 4x + x2 = 139 Factor a perfect square on the left side: (x + 2)(x + 2) = 139 Calculate the square root of the right side: 11.789826123 Break this problem into two subproblems by setting (x + 2) equal to 11.789826123 and -11.789826123.Subproblem 1
x + 2 = 11.789826123 Simplifying x + 2 = 11.789826123 Reorder the terms: 2 + x = 11.789826123 Solving 2 + x = 11.789826123 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 = 11.789826123 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.789826123 + -2 x = 11.789826123 + -2 Combine like terms: 11.789826123 + -2 = 9.789826123 x = 9.789826123 Simplifying x = 9.789826123Subproblem 2
x + 2 = -11.789826123 Simplifying x + 2 = -11.789826123 Reorder the terms: 2 + x = -11.789826123 Solving 2 + x = -11.789826123 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 = -11.789826123 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.789826123 + -2 x = -11.789826123 + -2 Combine like terms: -11.789826123 + -2 = -13.789826123 x = -13.789826123 Simplifying x = -13.789826123Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.789826123, -13.789826123}
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