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Simplifying 2x2 + 42x + -1079 = 0 Reorder the terms: -1079 + 42x + 2x2 = 0 Solving -1079 + 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'. -539.5 + 21x + x2 = 0 Move the constant term to the right: Add '539.5' to each side of the equation. -539.5 + 21x + 539.5 + x2 = 0 + 539.5 Reorder the terms: -539.5 + 539.5 + 21x + x2 = 0 + 539.5 Combine like terms: -539.5 + 539.5 = 0.0 0.0 + 21x + x2 = 0 + 539.5 21x + x2 = 0 + 539.5 Combine like terms: 0 + 539.5 = 539.5 21x + x2 = 539.5 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 = 539.5 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 539.5 + 110.25 Combine like terms: 539.5 + 110.25 = 649.75 110.25 + 21x + x2 = 649.75 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 649.75 Calculate the square root of the right side: 25.490194193 Break this problem into two subproblems by setting (x + 10.5) equal to 25.490194193 and -25.490194193.Subproblem 1
x + 10.5 = 25.490194193 Simplifying x + 10.5 = 25.490194193 Reorder the terms: 10.5 + x = 25.490194193 Solving 10.5 + x = 25.490194193 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 = 25.490194193 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 25.490194193 + -10.5 x = 25.490194193 + -10.5 Combine like terms: 25.490194193 + -10.5 = 14.990194193 x = 14.990194193 Simplifying x = 14.990194193Subproblem 2
x + 10.5 = -25.490194193 Simplifying x + 10.5 = -25.490194193 Reorder the terms: 10.5 + x = -25.490194193 Solving 10.5 + x = -25.490194193 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 = -25.490194193 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -25.490194193 + -10.5 x = -25.490194193 + -10.5 Combine like terms: -25.490194193 + -10.5 = -35.990194193 x = -35.990194193 Simplifying x = -35.990194193Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.990194193, -35.990194193}
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