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Simplifying x(x + 4) = 136 Reorder the terms: x(4 + x) = 136 (4 * x + x * x) = 136 (4x + x2) = 136 Solving 4x + x2 = 136 Solving for variable 'x'. Reorder the terms: -136 + 4x + x2 = 136 + -136 Combine like terms: 136 + -136 = 0 -136 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + 4x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + 4x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + 4x + x2 = 0 + 136 4x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 4x + x2 = 136 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 = 136 + 4 Reorder the terms: 4 + 4x + x2 = 136 + 4 Combine like terms: 136 + 4 = 140 4 + 4x + x2 = 140 Factor a perfect square on the left side: (x + 2)(x + 2) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x + 2) equal to 11.832159566 and -11.832159566.Subproblem 1
x + 2 = 11.832159566 Simplifying x + 2 = 11.832159566 Reorder the terms: 2 + x = 11.832159566 Solving 2 + x = 11.832159566 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 = 11.832159566 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.832159566 + -2 x = 11.832159566 + -2 Combine like terms: 11.832159566 + -2 = 9.832159566 x = 9.832159566 Simplifying x = 9.832159566Subproblem 2
x + 2 = -11.832159566 Simplifying x + 2 = -11.832159566 Reorder the terms: 2 + x = -11.832159566 Solving 2 + x = -11.832159566 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 = -11.832159566 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.832159566 + -2 x = -11.832159566 + -2 Combine like terms: -11.832159566 + -2 = -13.832159566 x = -13.832159566 Simplifying x = -13.832159566Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.832159566, -13.832159566}
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