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Simplifying 0 = -7x2 + 2x + 6 Reorder the terms: 0 = 6 + 2x + -7x2 Solving 0 = 6 + 2x + -7x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -2x + 7x2 = 6 + 2x + -7x2 + -6 + -2x + 7x2 Reorder the terms: -6 + -2x + 7x2 = 6 + -6 + 2x + -2x + -7x2 + 7x2 Combine like terms: 6 + -6 = 0 -6 + -2x + 7x2 = 0 + 2x + -2x + -7x2 + 7x2 -6 + -2x + 7x2 = 2x + -2x + -7x2 + 7x2 Combine like terms: 2x + -2x = 0 -6 + -2x + 7x2 = 0 + -7x2 + 7x2 -6 + -2x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -6 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -0.2857142857x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -0.2857142857x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + 0.8571428571 -0.2857142857x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -0.2857142857x + x2 = 0.8571428571 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.8571428571 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.8571428571 + 0.02040816328 Combine like terms: 0.8571428571 + 0.02040816328 = 0.87755102038 0.02040816328 + -0.2857142857x + x2 = 0.87755102038 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.87755102038 Calculate the square root of the right side: 0.936776932 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.936776932 and -0.936776932.Subproblem 1
x + -0.1428571429 = 0.936776932 Simplifying x + -0.1428571429 = 0.936776932 Reorder the terms: -0.1428571429 + x = 0.936776932 Solving -0.1428571429 + x = 0.936776932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.936776932 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.936776932 + 0.1428571429 x = 0.936776932 + 0.1428571429 Combine like terms: 0.936776932 + 0.1428571429 = 1.0796340749 x = 1.0796340749 Simplifying x = 1.0796340749Subproblem 2
x + -0.1428571429 = -0.936776932 Simplifying x + -0.1428571429 = -0.936776932 Reorder the terms: -0.1428571429 + x = -0.936776932 Solving -0.1428571429 + x = -0.936776932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.936776932 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.936776932 + 0.1428571429 x = -0.936776932 + 0.1428571429 Combine like terms: -0.936776932 + 0.1428571429 = -0.7939197891 x = -0.7939197891 Simplifying x = -0.7939197891Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0796340749, -0.7939197891}
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