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Simplifying x2 + 21x + -350 = 0 Reorder the terms: -350 + 21x + x2 = 0 Solving -350 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + 21x + 350 + x2 = 0 + 350 Reorder the terms: -350 + 350 + 21x + x2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + 21x + x2 = 0 + 350 21x + x2 = 0 + 350 Combine like terms: 0 + 350 = 350 21x + x2 = 350 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 350 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 350 + 110.25 Combine like terms: 350 + 110.25 = 460.25 110.25 + 21x + x2 = 460.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 460.25 Calculate the square root of the right side: 21.453437953 Break this problem into two subproblems by setting (x + 10.5) equal to 21.453437953 and -21.453437953.Subproblem 1
x + 10.5 = 21.453437953 Simplifying x + 10.5 = 21.453437953 Reorder the terms: 10.5 + x = 21.453437953 Solving 10.5 + x = 21.453437953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 21.453437953 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 21.453437953 + -10.5 x = 21.453437953 + -10.5 Combine like terms: 21.453437953 + -10.5 = 10.953437953 x = 10.953437953 Simplifying x = 10.953437953Subproblem 2
x + 10.5 = -21.453437953 Simplifying x + 10.5 = -21.453437953 Reorder the terms: 10.5 + x = -21.453437953 Solving 10.5 + x = -21.453437953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -21.453437953 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -21.453437953 + -10.5 x = -21.453437953 + -10.5 Combine like terms: -21.453437953 + -10.5 = -31.953437953 x = -31.953437953 Simplifying x = -31.953437953Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.953437953, -31.953437953}
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