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Simplifying -4.9x2 + -43.4x + -6.3 = 0 Reorder the terms: -6.3 + -43.4x + -4.9x2 = 0 Solving -6.3 + -43.4x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 1.285714286 + 8.857142857x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + 8.857142857x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + 8.857142857x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + 8.857142857x + x2 = 0 + -1.285714286 8.857142857x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 8.857142857x + x2 = -1.285714286 The x term is 8.857142857x. Take half its coefficient (4.428571429). Square it (19.61224490) and add it to both sides. Add '19.61224490' to each side of the equation. 8.857142857x + 19.61224490 + x2 = -1.285714286 + 19.61224490 Reorder the terms: 19.61224490 + 8.857142857x + x2 = -1.285714286 + 19.61224490 Combine like terms: -1.285714286 + 19.61224490 = 18.326530614 19.61224490 + 8.857142857x + x2 = 18.326530614 Factor a perfect square on the left side: (x + 4.428571429)(x + 4.428571429) = 18.326530614 Calculate the square root of the right side: 4.280949733 Break this problem into two subproblems by setting (x + 4.428571429) equal to 4.280949733 and -4.280949733.Subproblem 1
x + 4.428571429 = 4.280949733 Simplifying x + 4.428571429 = 4.280949733 Reorder the terms: 4.428571429 + x = 4.280949733 Solving 4.428571429 + x = 4.280949733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.428571429' to each side of the equation. 4.428571429 + -4.428571429 + x = 4.280949733 + -4.428571429 Combine like terms: 4.428571429 + -4.428571429 = 0.000000000 0.000000000 + x = 4.280949733 + -4.428571429 x = 4.280949733 + -4.428571429 Combine like terms: 4.280949733 + -4.428571429 = -0.147621696 x = -0.147621696 Simplifying x = -0.147621696Subproblem 2
x + 4.428571429 = -4.280949733 Simplifying x + 4.428571429 = -4.280949733 Reorder the terms: 4.428571429 + x = -4.280949733 Solving 4.428571429 + x = -4.280949733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.428571429' to each side of the equation. 4.428571429 + -4.428571429 + x = -4.280949733 + -4.428571429 Combine like terms: 4.428571429 + -4.428571429 = 0.000000000 0.000000000 + x = -4.280949733 + -4.428571429 x = -4.280949733 + -4.428571429 Combine like terms: -4.280949733 + -4.428571429 = -8.709521162 x = -8.709521162 Simplifying x = -8.709521162Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.147621696, -8.709521162}
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