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Simplifying x(x + 6) = 50 Reorder the terms: x(6 + x) = 50 (6 * x + x * x) = 50 (6x + x2) = 50 Solving 6x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 6x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 6x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 6x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 6x + x2 = 0 + 50 6x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 6x + x2 = 50 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 50 + 9 Reorder the terms: 9 + 6x + x2 = 50 + 9 Combine like terms: 50 + 9 = 59 9 + 6x + x2 = 59 Factor a perfect square on the left side: (x + 3)(x + 3) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + 3) equal to 7.681145748 and -7.681145748.Subproblem 1
x + 3 = 7.681145748 Simplifying x + 3 = 7.681145748 Reorder the terms: 3 + x = 7.681145748 Solving 3 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.681145748 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.681145748 + -3 x = 7.681145748 + -3 Combine like terms: 7.681145748 + -3 = 4.681145748 x = 4.681145748 Simplifying x = 4.681145748Subproblem 2
x + 3 = -7.681145748 Simplifying x + 3 = -7.681145748 Reorder the terms: 3 + x = -7.681145748 Solving 3 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.681145748 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.681145748 + -3 x = -7.681145748 + -3 Combine like terms: -7.681145748 + -3 = -10.681145748 x = -10.681145748 Simplifying x = -10.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.681145748, -10.681145748}
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