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Simplifying x2 + -6x = 29 Reorder the terms: -6x + x2 = 29 Solving -6x + x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + -6x + x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -6x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -6x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -6x + x2 = 0 + 29 -6x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -6x + x2 = 29 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 = 29 + 9 Reorder the terms: 9 + -6x + x2 = 29 + 9 Combine like terms: 29 + 9 = 38 9 + -6x + x2 = 38 Factor a perfect square on the left side: (x + -3)(x + -3) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + -3) equal to 6.164414003 and -6.164414003.Subproblem 1
x + -3 = 6.164414003 Simplifying x + -3 = 6.164414003 Reorder the terms: -3 + x = 6.164414003 Solving -3 + x = 6.164414003 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 = 6.164414003 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.164414003 + 3 x = 6.164414003 + 3 Combine like terms: 6.164414003 + 3 = 9.164414003 x = 9.164414003 Simplifying x = 9.164414003Subproblem 2
x + -3 = -6.164414003 Simplifying x + -3 = -6.164414003 Reorder the terms: -3 + x = -6.164414003 Solving -3 + x = -6.164414003 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 = -6.164414003 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.164414003 + 3 x = -6.164414003 + 3 Combine like terms: -6.164414003 + 3 = -3.164414003 x = -3.164414003 Simplifying x = -3.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.164414003, -3.164414003}
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