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Simplifying 0 = -7x2 + 7x + 6 Reorder the terms: 0 = 6 + 7x + -7x2 Solving 0 = 6 + 7x + -7x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -7x + 7x2 = 6 + 7x + -7x2 + -6 + -7x + 7x2 Reorder the terms: -6 + -7x + 7x2 = 6 + -6 + 7x + -7x + -7x2 + 7x2 Combine like terms: 6 + -6 = 0 -6 + -7x + 7x2 = 0 + 7x + -7x + -7x2 + 7x2 -6 + -7x + 7x2 = 7x + -7x + -7x2 + 7x2 Combine like terms: 7x + -7x = 0 -6 + -7x + 7x2 = 0 + -7x2 + 7x2 -6 + -7x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -6 + -7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -1x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -1x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -1x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.8571428571 -1x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -1x + x2 = 0.8571428571 The x term is -1x. 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. -1x + 0.25 + x2 = 0.8571428571 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.8571428571 + 0.25 Combine like terms: 0.8571428571 + 0.25 = 1.1071428571 0.25 + -1x + 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 = 1.552208562 x = 1.552208562 Simplifying x = 1.552208562Subproblem 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 = -0.552208562 x = -0.552208562 Simplifying x = -0.552208562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.552208562, -0.552208562}
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