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Simplifying 49x2 + 70x + -9 = 0 Reorder the terms: -9 + 70x + 49x2 = 0 Solving -9 + 70x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.1836734694 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '0.1836734694' to each side of the equation. -0.1836734694 + 1.428571429x + 0.1836734694 + x2 = 0 + 0.1836734694 Reorder the terms: -0.1836734694 + 0.1836734694 + 1.428571429x + x2 = 0 + 0.1836734694 Combine like terms: -0.1836734694 + 0.1836734694 = 0.0000000000 0.0000000000 + 1.428571429x + x2 = 0 + 0.1836734694 1.428571429x + x2 = 0 + 0.1836734694 Combine like terms: 0 + 0.1836734694 = 0.1836734694 1.428571429x + x2 = 0.1836734694 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 = 0.1836734694 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 0.1836734694 + 0.5102040819 Combine like terms: 0.1836734694 + 0.5102040819 = 0.6938775513 0.5102040819 + 1.428571429x + x2 = 0.6938775513 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 0.6938775513 Calculate the square root of the right side: 0.832993128 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 0.832993128 and -0.832993128.Subproblem 1
x + 0.7142857145 = 0.832993128 Simplifying x + 0.7142857145 = 0.832993128 Reorder the terms: 0.7142857145 + x = 0.832993128 Solving 0.7142857145 + x = 0.832993128 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 = 0.832993128 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 0.832993128 + -0.7142857145 x = 0.832993128 + -0.7142857145 Combine like terms: 0.832993128 + -0.7142857145 = 0.1187074135 x = 0.1187074135 Simplifying x = 0.1187074135Subproblem 2
x + 0.7142857145 = -0.832993128 Simplifying x + 0.7142857145 = -0.832993128 Reorder the terms: 0.7142857145 + x = -0.832993128 Solving 0.7142857145 + x = -0.832993128 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 = -0.832993128 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -0.832993128 + -0.7142857145 x = -0.832993128 + -0.7142857145 Combine like terms: -0.832993128 + -0.7142857145 = -1.5472788425 x = -1.5472788425 Simplifying x = -1.5472788425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1187074135, -1.5472788425}
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