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Simplifying 7x2 + 7x + -11 = 0 Reorder the terms: -11 + 7x + 7x2 = 0 Solving -11 + 7x + 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'. -1.571428571 + x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + x + x2 = 0 + 1.571428571 x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 x + x2 = 1.571428571 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.571428571 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.571428571 + 0.25 Combine like terms: 1.571428571 + 0.25 = 1.821428571 1.25 + x2 = 1.821428571 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.821428571 Calculate the square root of the right side: 1.349603116 Break this problem into two subproblems by setting (x + 0.5) equal to 1.349603116 and -1.349603116.Subproblem 1
x + 0.5 = 1.349603116 Simplifying x + 0.5 = 1.349603116 Reorder the terms: 0.5 + x = 1.349603116 Solving 0.5 + x = 1.349603116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.349603116 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.349603116 + -0.5 x = 1.349603116 + -0.5 Combine like terms: 1.349603116 + -0.5 = 0.849603116 x = 0.849603116 Simplifying x = 0.849603116Subproblem 2
x + 0.5 = -1.349603116 Simplifying x + 0.5 = -1.349603116 Reorder the terms: 0.5 + x = -1.349603116 Solving 0.5 + x = -1.349603116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.349603116 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.349603116 + -0.5 x = -1.349603116 + -0.5 Combine like terms: -1.349603116 + -0.5 = -1.849603116 x = -1.849603116 Simplifying x = -1.849603116Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.849603116, -1.849603116}
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