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Simplifying 35x2 + -73x + -90 = 0 Reorder the terms: -90 + -73x + 35x2 = 0 Solving -90 + -73x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -2.571428571 + -2.085714286x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -2.085714286x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -2.085714286x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -2.085714286x + x2 = 0 + 2.571428571 -2.085714286x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -2.085714286x + x2 = 2.571428571 The x term is -2.085714286x. Take half its coefficient (-1.042857143). Square it (1.087551021) and add it to both sides. Add '1.087551021' to each side of the equation. -2.085714286x + 1.087551021 + x2 = 2.571428571 + 1.087551021 Reorder the terms: 1.087551021 + -2.085714286x + x2 = 2.571428571 + 1.087551021 Combine like terms: 2.571428571 + 1.087551021 = 3.658979592 1.087551021 + -2.085714286x + x2 = 3.658979592 Factor a perfect square on the left side: (x + -1.042857143)(x + -1.042857143) = 3.658979592 Calculate the square root of the right side: 1.91284594 Break this problem into two subproblems by setting (x + -1.042857143) equal to 1.91284594 and -1.91284594.Subproblem 1
x + -1.042857143 = 1.91284594 Simplifying x + -1.042857143 = 1.91284594 Reorder the terms: -1.042857143 + x = 1.91284594 Solving -1.042857143 + x = 1.91284594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.042857143' to each side of the equation. -1.042857143 + 1.042857143 + x = 1.91284594 + 1.042857143 Combine like terms: -1.042857143 + 1.042857143 = 0.000000000 0.000000000 + x = 1.91284594 + 1.042857143 x = 1.91284594 + 1.042857143 Combine like terms: 1.91284594 + 1.042857143 = 2.955703083 x = 2.955703083 Simplifying x = 2.955703083Subproblem 2
x + -1.042857143 = -1.91284594 Simplifying x + -1.042857143 = -1.91284594 Reorder the terms: -1.042857143 + x = -1.91284594 Solving -1.042857143 + x = -1.91284594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.042857143' to each side of the equation. -1.042857143 + 1.042857143 + x = -1.91284594 + 1.042857143 Combine like terms: -1.042857143 + 1.042857143 = 0.000000000 0.000000000 + x = -1.91284594 + 1.042857143 x = -1.91284594 + 1.042857143 Combine like terms: -1.91284594 + 1.042857143 = -0.869988797 x = -0.869988797 Simplifying x = -0.869988797Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.955703083, -0.869988797}
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