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Simplifying 14x(10x + 7) = 93 Reorder the terms: 14x(7 + 10x) = 93 (7 * 14x + 10x * 14x) = 93 (98x + 140x2) = 93 Solving 98x + 140x2 = 93 Solving for variable 'x'. Reorder the terms: -93 + 98x + 140x2 = 93 + -93 Combine like terms: 93 + -93 = 0 -93 + 98x + 140x2 = 0 Begin completing the square. Divide all terms by 140 the coefficient of the squared term: Divide each side by '140'. -0.6642857143 + 0.7x + x2 = 0.0 Move the constant term to the right: Add '0.6642857143' to each side of the equation. -0.6642857143 + 0.7x + 0.6642857143 + x2 = 0.0 + 0.6642857143 Reorder the terms: -0.6642857143 + 0.6642857143 + 0.7x + x2 = 0.0 + 0.6642857143 Combine like terms: -0.6642857143 + 0.6642857143 = 0.0000000000 0.0000000000 + 0.7x + x2 = 0.0 + 0.6642857143 0.7x + x2 = 0.0 + 0.6642857143 Combine like terms: 0.0 + 0.6642857143 = 0.6642857143 0.7x + x2 = 0.6642857143 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 0.6642857143 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 0.6642857143 + 0.1225 Combine like terms: 0.6642857143 + 0.1225 = 0.7867857143 0.1225 + 0.7x + x2 = 0.7867857143 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 0.7867857143 Calculate the square root of the right side: 0.887009422 Break this problem into two subproblems by setting (x + 0.35) equal to 0.887009422 and -0.887009422.Subproblem 1
x + 0.35 = 0.887009422 Simplifying x + 0.35 = 0.887009422 Reorder the terms: 0.35 + x = 0.887009422 Solving 0.35 + x = 0.887009422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.887009422 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.887009422 + -0.35 x = 0.887009422 + -0.35 Combine like terms: 0.887009422 + -0.35 = 0.537009422 x = 0.537009422 Simplifying x = 0.537009422Subproblem 2
x + 0.35 = -0.887009422 Simplifying x + 0.35 = -0.887009422 Reorder the terms: 0.35 + x = -0.887009422 Solving 0.35 + x = -0.887009422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.887009422 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.887009422 + -0.35 x = -0.887009422 + -0.35 Combine like terms: -0.887009422 + -0.35 = -1.237009422 x = -1.237009422 Simplifying x = -1.237009422Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.537009422, -1.237009422}
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