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Simplifying 7x2 + 7x + -6 = 0 Reorder the terms: -6 + 7x + 7x2 = 0 Solving -6 + 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'. -0.8571428571 + x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.8571428571 x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 x + x2 = 0.8571428571 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 = 0.8571428571 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.8571428571 + 0.25 Combine like terms: 0.8571428571 + 0.25 = 1.1071428571 1.25 + x2 = 1.1071428571 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.1071428571 Calculate the square root of the right side: 1.052208562 Break this problem into two subproblems by setting (x + 0.5) equal to 1.052208562 and -1.052208562.Subproblem 1
x + 0.5 = 1.052208562 Simplifying x + 0.5 = 1.052208562 Reorder the terms: 0.5 + x = 1.052208562 Solving 0.5 + x = 1.052208562 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 = 1.052208562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.052208562 + -0.5 x = 1.052208562 + -0.5 Combine like terms: 1.052208562 + -0.5 = 0.552208562 x = 0.552208562 Simplifying x = 0.552208562Subproblem 2
x + 0.5 = -1.052208562 Simplifying x + 0.5 = -1.052208562 Reorder the terms: 0.5 + x = -1.052208562 Solving 0.5 + x = -1.052208562 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 = -1.052208562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.052208562 + -0.5 x = -1.052208562 + -0.5 Combine like terms: -1.052208562 + -0.5 = -1.552208562 x = -1.552208562 Simplifying x = -1.552208562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.552208562, -1.552208562}
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