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Simplifying x2 + 42x + -9 = 0 Reorder the terms: -9 + 42x + x2 = 0 Solving -9 + 42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 42x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 42x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 42x + x2 = 0 + 9 42x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 42x + x2 = 9 The x term is 42x. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42x + 441 + x2 = 9 + 441 Reorder the terms: 441 + 42x + x2 = 9 + 441 Combine like terms: 9 + 441 = 450 441 + 42x + x2 = 450 Factor a perfect square on the left side: (x + 21)(x + 21) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (x + 21) equal to 21.213203436 and -21.213203436.Subproblem 1
x + 21 = 21.213203436 Simplifying x + 21 = 21.213203436 Reorder the terms: 21 + x = 21.213203436 Solving 21 + x = 21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 21.213203436 + -21 Combine like terms: 21 + -21 = 0 0 + x = 21.213203436 + -21 x = 21.213203436 + -21 Combine like terms: 21.213203436 + -21 = 0.213203436 x = 0.213203436 Simplifying x = 0.213203436Subproblem 2
x + 21 = -21.213203436 Simplifying x + 21 = -21.213203436 Reorder the terms: 21 + x = -21.213203436 Solving 21 + x = -21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -21.213203436 + -21 Combine like terms: 21 + -21 = 0 0 + x = -21.213203436 + -21 x = -21.213203436 + -21 Combine like terms: -21.213203436 + -21 = -42.213203436 x = -42.213203436 Simplifying x = -42.213203436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.213203436, -42.213203436}
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