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Simplifying x + x + x(x + 2) = 51 Reorder the terms: x + x + x(2 + x) = 51 x + x + (2 * x + x * x) = 51 x + x + (2x + x2) = 51 Combine like terms: x + x = 2x 2x + 2x + x2 = 51 Combine like terms: 2x + 2x = 4x 4x + x2 = 51 Solving 4x + x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + 4x + x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 4x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 4x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 4x + x2 = 0 + 51 4x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 4x + x2 = 51 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 = 51 + 4 Reorder the terms: 4 + 4x + x2 = 51 + 4 Combine like terms: 51 + 4 = 55 4 + 4x + x2 = 55 Factor a perfect square on the left side: (x + 2)(x + 2) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + 2) equal to 7.416198487 and -7.416198487.Subproblem 1
x + 2 = 7.416198487 Simplifying x + 2 = 7.416198487 Reorder the terms: 2 + x = 7.416198487 Solving 2 + x = 7.416198487 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 = 7.416198487 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.416198487 + -2 x = 7.416198487 + -2 Combine like terms: 7.416198487 + -2 = 5.416198487 x = 5.416198487 Simplifying x = 5.416198487Subproblem 2
x + 2 = -7.416198487 Simplifying x + 2 = -7.416198487 Reorder the terms: 2 + x = -7.416198487 Solving 2 + x = -7.416198487 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 = -7.416198487 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.416198487 + -2 x = -7.416198487 + -2 Combine like terms: -7.416198487 + -2 = -9.416198487 x = -9.416198487 Simplifying x = -9.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.416198487, -9.416198487}
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