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Simplifying x2 + 4x = 297 Reorder the terms: 4x + x2 = 297 Solving 4x + x2 = 297 Solving for variable 'x'. Reorder the terms: -297 + 4x + x2 = 297 + -297 Combine like terms: 297 + -297 = 0 -297 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '297' to each side of the equation. -297 + 4x + 297 + x2 = 0 + 297 Reorder the terms: -297 + 297 + 4x + x2 = 0 + 297 Combine like terms: -297 + 297 = 0 0 + 4x + x2 = 0 + 297 4x + x2 = 0 + 297 Combine like terms: 0 + 297 = 297 4x + x2 = 297 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 = 297 + 4 Reorder the terms: 4 + 4x + x2 = 297 + 4 Combine like terms: 297 + 4 = 301 4 + 4x + x2 = 301 Factor a perfect square on the left side: (x + 2)(x + 2) = 301 Calculate the square root of the right side: 17.349351573 Break this problem into two subproblems by setting (x + 2) equal to 17.349351573 and -17.349351573.Subproblem 1
x + 2 = 17.349351573 Simplifying x + 2 = 17.349351573 Reorder the terms: 2 + x = 17.349351573 Solving 2 + x = 17.349351573 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 = 17.349351573 + -2 Combine like terms: 2 + -2 = 0 0 + x = 17.349351573 + -2 x = 17.349351573 + -2 Combine like terms: 17.349351573 + -2 = 15.349351573 x = 15.349351573 Simplifying x = 15.349351573Subproblem 2
x + 2 = -17.349351573 Simplifying x + 2 = -17.349351573 Reorder the terms: 2 + x = -17.349351573 Solving 2 + x = -17.349351573 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 = -17.349351573 + -2 Combine like terms: 2 + -2 = 0 0 + x = -17.349351573 + -2 x = -17.349351573 + -2 Combine like terms: -17.349351573 + -2 = -19.349351573 x = -19.349351573 Simplifying x = -19.349351573Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.349351573, -19.349351573}
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