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Simplifying 35x2 + -77x + -6 = 0 Reorder the terms: -6 + -77x + 35x2 = 0 Solving -6 + -77x + 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'. -0.1714285714 + -2.2x + x2 = 0 Move the constant term to the right: Add '0.1714285714' to each side of the equation. -0.1714285714 + -2.2x + 0.1714285714 + x2 = 0 + 0.1714285714 Reorder the terms: -0.1714285714 + 0.1714285714 + -2.2x + x2 = 0 + 0.1714285714 Combine like terms: -0.1714285714 + 0.1714285714 = 0.0000000000 0.0000000000 + -2.2x + x2 = 0 + 0.1714285714 -2.2x + x2 = 0 + 0.1714285714 Combine like terms: 0 + 0.1714285714 = 0.1714285714 -2.2x + x2 = 0.1714285714 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 0.1714285714 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 0.1714285714 + 1.21 Combine like terms: 0.1714285714 + 1.21 = 1.3814285714 1.21 + -2.2x + x2 = 1.3814285714 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 1.3814285714 Calculate the square root of the right side: 1.175341896 Break this problem into two subproblems by setting (x + -1.1) equal to 1.175341896 and -1.175341896.Subproblem 1
x + -1.1 = 1.175341896 Simplifying x + -1.1 = 1.175341896 Reorder the terms: -1.1 + x = 1.175341896 Solving -1.1 + x = 1.175341896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 1.175341896 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 1.175341896 + 1.1 x = 1.175341896 + 1.1 Combine like terms: 1.175341896 + 1.1 = 2.275341896 x = 2.275341896 Simplifying x = 2.275341896Subproblem 2
x + -1.1 = -1.175341896 Simplifying x + -1.1 = -1.175341896 Reorder the terms: -1.1 + x = -1.175341896 Solving -1.1 + x = -1.175341896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -1.175341896 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -1.175341896 + 1.1 x = -1.175341896 + 1.1 Combine like terms: -1.175341896 + 1.1 = -0.075341896 x = -0.075341896 Simplifying x = -0.075341896Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.275341896, -0.075341896}
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