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Simplifying 7x2 + 2x + -81 = 0 Reorder the terms: -81 + 2x + 7x2 = 0 Solving -81 + 2x + 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'. -11.57142857 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '11.57142857' to each side of the equation. -11.57142857 + 0.2857142857x + 11.57142857 + x2 = 0 + 11.57142857 Reorder the terms: -11.57142857 + 11.57142857 + 0.2857142857x + x2 = 0 + 11.57142857 Combine like terms: -11.57142857 + 11.57142857 = 0.00000000 0.00000000 + 0.2857142857x + x2 = 0 + 11.57142857 0.2857142857x + x2 = 0 + 11.57142857 Combine like terms: 0 + 11.57142857 = 11.57142857 0.2857142857x + x2 = 11.57142857 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 = 11.57142857 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 11.57142857 + 0.02040816328 Combine like terms: 11.57142857 + 0.02040816328 = 11.59183673328 0.02040816328 + 0.2857142857x + x2 = 11.59183673328 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 11.59183673328 Calculate the square root of the right side: 3.404678653 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 3.404678653 and -3.404678653.Subproblem 1
x + 0.1428571429 = 3.404678653 Simplifying x + 0.1428571429 = 3.404678653 Reorder the terms: 0.1428571429 + x = 3.404678653 Solving 0.1428571429 + x = 3.404678653 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 = 3.404678653 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 3.404678653 + -0.1428571429 x = 3.404678653 + -0.1428571429 Combine like terms: 3.404678653 + -0.1428571429 = 3.2618215101 x = 3.2618215101 Simplifying x = 3.2618215101Subproblem 2
x + 0.1428571429 = -3.404678653 Simplifying x + 0.1428571429 = -3.404678653 Reorder the terms: 0.1428571429 + x = -3.404678653 Solving 0.1428571429 + x = -3.404678653 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 = -3.404678653 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -3.404678653 + -0.1428571429 x = -3.404678653 + -0.1428571429 Combine like terms: -3.404678653 + -0.1428571429 = -3.5475357959 x = -3.5475357959 Simplifying x = -3.5475357959Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2618215101, -3.5475357959}
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