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Simplifying 6x + x2 = 45 Solving 6x + x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 6x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 6x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 6x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 6x + x2 = 0 + 45 6x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 6x + x2 = 45 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 = 45 + 9 Reorder the terms: 9 + 6x + x2 = 45 + 9 Combine like terms: 45 + 9 = 54 9 + 6x + x2 = 54 Factor a perfect square on the left side: (x + 3)(x + 3) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + 3) equal to 7.348469228 and -7.348469228.Subproblem 1
x + 3 = 7.348469228 Simplifying x + 3 = 7.348469228 Reorder the terms: 3 + x = 7.348469228 Solving 3 + x = 7.348469228 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 = 7.348469228 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.348469228 + -3 x = 7.348469228 + -3 Combine like terms: 7.348469228 + -3 = 4.348469228 x = 4.348469228 Simplifying x = 4.348469228Subproblem 2
x + 3 = -7.348469228 Simplifying x + 3 = -7.348469228 Reorder the terms: 3 + x = -7.348469228 Solving 3 + x = -7.348469228 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 = -7.348469228 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.348469228 + -3 x = -7.348469228 + -3 Combine like terms: -7.348469228 + -3 = -10.348469228 x = -10.348469228 Simplifying x = -10.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.348469228, -10.348469228}
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