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Simplifying 2x2 + 42x + -57 = 0 Reorder the terms: -57 + 42x + 2x2 = 0 Solving -57 + 42x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28.5 + 21x + x2 = 0 Move the constant term to the right: Add '28.5' to each side of the equation. -28.5 + 21x + 28.5 + x2 = 0 + 28.5 Reorder the terms: -28.5 + 28.5 + 21x + x2 = 0 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + 21x + x2 = 0 + 28.5 21x + x2 = 0 + 28.5 Combine like terms: 0 + 28.5 = 28.5 21x + x2 = 28.5 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 = 28.5 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 28.5 + 110.25 Combine like terms: 28.5 + 110.25 = 138.75 110.25 + 21x + x2 = 138.75 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 138.75 Calculate the square root of the right side: 11.779218989 Break this problem into two subproblems by setting (x + 10.5) equal to 11.779218989 and -11.779218989.Subproblem 1
x + 10.5 = 11.779218989 Simplifying x + 10.5 = 11.779218989 Reorder the terms: 10.5 + x = 11.779218989 Solving 10.5 + x = 11.779218989 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 = 11.779218989 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 11.779218989 + -10.5 x = 11.779218989 + -10.5 Combine like terms: 11.779218989 + -10.5 = 1.279218989 x = 1.279218989 Simplifying x = 1.279218989Subproblem 2
x + 10.5 = -11.779218989 Simplifying x + 10.5 = -11.779218989 Reorder the terms: 10.5 + x = -11.779218989 Solving 10.5 + x = -11.779218989 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 = -11.779218989 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -11.779218989 + -10.5 x = -11.779218989 + -10.5 Combine like terms: -11.779218989 + -10.5 = -22.279218989 x = -22.279218989 Simplifying x = -22.279218989Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.279218989, -22.279218989}
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