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Simplifying 70x2 + 81x + -7 = 0 Reorder the terms: -7 + 81x + 70x2 = 0 Solving -7 + 81x + 70x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. -0.1 + 1.157142857x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 1.157142857x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 1.157142857x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 1.157142857x + x2 = 0 + 0.1 1.157142857x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 1.157142857x + x2 = 0.1 The x term is 1.157142857x. Take half its coefficient (0.5785714285). Square it (0.3347448979) and add it to both sides. Add '0.3347448979' to each side of the equation. 1.157142857x + 0.3347448979 + x2 = 0.1 + 0.3347448979 Reorder the terms: 0.3347448979 + 1.157142857x + x2 = 0.1 + 0.3347448979 Combine like terms: 0.1 + 0.3347448979 = 0.4347448979 0.3347448979 + 1.157142857x + x2 = 0.4347448979 Factor a perfect square on the left side: (x + 0.5785714285)(x + 0.5785714285) = 0.4347448979 Calculate the square root of the right side: 0.659351877 Break this problem into two subproblems by setting (x + 0.5785714285) equal to 0.659351877 and -0.659351877.Subproblem 1
x + 0.5785714285 = 0.659351877 Simplifying x + 0.5785714285 = 0.659351877 Reorder the terms: 0.5785714285 + x = 0.659351877 Solving 0.5785714285 + x = 0.659351877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5785714285' to each side of the equation. 0.5785714285 + -0.5785714285 + x = 0.659351877 + -0.5785714285 Combine like terms: 0.5785714285 + -0.5785714285 = 0.0000000000 0.0000000000 + x = 0.659351877 + -0.5785714285 x = 0.659351877 + -0.5785714285 Combine like terms: 0.659351877 + -0.5785714285 = 0.0807804485 x = 0.0807804485 Simplifying x = 0.0807804485Subproblem 2
x + 0.5785714285 = -0.659351877 Simplifying x + 0.5785714285 = -0.659351877 Reorder the terms: 0.5785714285 + x = -0.659351877 Solving 0.5785714285 + x = -0.659351877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5785714285' to each side of the equation. 0.5785714285 + -0.5785714285 + x = -0.659351877 + -0.5785714285 Combine like terms: 0.5785714285 + -0.5785714285 = 0.0000000000 0.0000000000 + x = -0.659351877 + -0.5785714285 x = -0.659351877 + -0.5785714285 Combine like terms: -0.659351877 + -0.5785714285 = -1.2379233055 x = -1.2379233055 Simplifying x = -1.2379233055Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0807804485, -1.2379233055}
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