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Simplifying 7x2 + 14x + -121 = 0 Reorder the terms: -121 + 14x + 7x2 = 0 Solving -121 + 14x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -17.28571429 + 2x + x2 = 0 Move the constant term to the right: Add '17.28571429' to each side of the equation. -17.28571429 + 2x + 17.28571429 + x2 = 0 + 17.28571429 Reorder the terms: -17.28571429 + 17.28571429 + 2x + x2 = 0 + 17.28571429 Combine like terms: -17.28571429 + 17.28571429 = 0.00000000 0.00000000 + 2x + x2 = 0 + 17.28571429 2x + x2 = 0 + 17.28571429 Combine like terms: 0 + 17.28571429 = 17.28571429 2x + x2 = 17.28571429 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 17.28571429 + 1 Reorder the terms: 1 + 2x + x2 = 17.28571429 + 1 Combine like terms: 17.28571429 + 1 = 18.28571429 1 + 2x + x2 = 18.28571429 Factor a perfect square on the left side: (x + 1)(x + 1) = 18.28571429 Calculate the square root of the right side: 4.276179871 Break this problem into two subproblems by setting (x + 1) equal to 4.276179871 and -4.276179871.Subproblem 1
x + 1 = 4.276179871 Simplifying x + 1 = 4.276179871 Reorder the terms: 1 + x = 4.276179871 Solving 1 + x = 4.276179871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.276179871 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.276179871 + -1 x = 4.276179871 + -1 Combine like terms: 4.276179871 + -1 = 3.276179871 x = 3.276179871 Simplifying x = 3.276179871Subproblem 2
x + 1 = -4.276179871 Simplifying x + 1 = -4.276179871 Reorder the terms: 1 + x = -4.276179871 Solving 1 + x = -4.276179871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.276179871 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.276179871 + -1 x = -4.276179871 + -1 Combine like terms: -4.276179871 + -1 = -5.276179871 x = -5.276179871 Simplifying x = -5.276179871Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.276179871, -5.276179871}
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