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Simplifying x(x + 4) = 149 Reorder the terms: x(4 + x) = 149 (4 * x + x * x) = 149 (4x + x2) = 149 Solving 4x + x2 = 149 Solving for variable 'x'. Reorder the terms: -149 + 4x + x2 = 149 + -149 Combine like terms: 149 + -149 = 0 -149 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '149' to each side of the equation. -149 + 4x + 149 + x2 = 0 + 149 Reorder the terms: -149 + 149 + 4x + x2 = 0 + 149 Combine like terms: -149 + 149 = 0 0 + 4x + x2 = 0 + 149 4x + x2 = 0 + 149 Combine like terms: 0 + 149 = 149 4x + x2 = 149 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 = 149 + 4 Reorder the terms: 4 + 4x + x2 = 149 + 4 Combine like terms: 149 + 4 = 153 4 + 4x + x2 = 153 Factor a perfect square on the left side: (x + 2)(x + 2) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + 2) equal to 12.369316877 and -12.369316877.Subproblem 1
x + 2 = 12.369316877 Simplifying x + 2 = 12.369316877 Reorder the terms: 2 + x = 12.369316877 Solving 2 + x = 12.369316877 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 = 12.369316877 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.369316877 + -2 x = 12.369316877 + -2 Combine like terms: 12.369316877 + -2 = 10.369316877 x = 10.369316877 Simplifying x = 10.369316877Subproblem 2
x + 2 = -12.369316877 Simplifying x + 2 = -12.369316877 Reorder the terms: 2 + x = -12.369316877 Solving 2 + x = -12.369316877 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 = -12.369316877 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.369316877 + -2 x = -12.369316877 + -2 Combine like terms: -12.369316877 + -2 = -14.369316877 x = -14.369316877 Simplifying x = -14.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.369316877, -14.369316877}
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