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Simplifying 49x2 + 70x = 6 Reorder the terms: 70x + 49x2 = 6 Solving 70x + 49x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 70x + 49x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 70x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.1224489796 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '0.1224489796' to each side of the equation. -0.1224489796 + 1.428571429x + 0.1224489796 + x2 = 0 + 0.1224489796 Reorder the terms: -0.1224489796 + 0.1224489796 + 1.428571429x + x2 = 0 + 0.1224489796 Combine like terms: -0.1224489796 + 0.1224489796 = 0.0000000000 0.0000000000 + 1.428571429x + x2 = 0 + 0.1224489796 1.428571429x + x2 = 0 + 0.1224489796 Combine like terms: 0 + 0.1224489796 = 0.1224489796 1.428571429x + x2 = 0.1224489796 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 0.1224489796 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 0.1224489796 + 0.5102040819 Combine like terms: 0.1224489796 + 0.5102040819 = 0.6326530615 0.5102040819 + 1.428571429x + x2 = 0.6326530615 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 0.6326530615 Calculate the square root of the right side: 0.795394909 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 0.795394909 and -0.795394909.Subproblem 1
x + 0.7142857145 = 0.795394909 Simplifying x + 0.7142857145 = 0.795394909 Reorder the terms: 0.7142857145 + x = 0.795394909 Solving 0.7142857145 + x = 0.795394909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 0.795394909 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 0.795394909 + -0.7142857145 x = 0.795394909 + -0.7142857145 Combine like terms: 0.795394909 + -0.7142857145 = 0.0811091945 x = 0.0811091945 Simplifying x = 0.0811091945Subproblem 2
x + 0.7142857145 = -0.795394909 Simplifying x + 0.7142857145 = -0.795394909 Reorder the terms: 0.7142857145 + x = -0.795394909 Solving 0.7142857145 + x = -0.795394909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -0.795394909 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -0.795394909 + -0.7142857145 x = -0.795394909 + -0.7142857145 Combine like terms: -0.795394909 + -0.7142857145 = -1.5096806235 x = -1.5096806235 Simplifying x = -1.5096806235Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0811091945, -1.5096806235}
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