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Simplifying 7(7x2 + 2x + -6) = 0 Reorder the terms: 7(-6 + 2x + 7x2) = 0 (-6 * 7 + 2x * 7 + 7x2 * 7) = 0 (-42 + 14x + 49x2) = 0 Solving -42 + 14x + 49x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-6 + 2x + 7x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-6 + 2x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + 2x + 7x2 = 0 Solving -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 = 0.7939197891 x = 0.7939197891 Simplifying x = 0.7939197891Subproblem 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 = -1.0796340749 x = -1.0796340749 Simplifying x = -1.0796340749Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7939197891, -1.0796340749}Solution
x = {0.7939197891, -1.0796340749}
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