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Simplifying 7x2 + -14x + -19 = 0 Reorder the terms: -19 + -14x + 7x2 = 0 Solving -19 + -14x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.714285714 + -2x + x2 = 0 Move the constant term to the right: Add '2.714285714' to each side of the equation. -2.714285714 + -2x + 2.714285714 + x2 = 0 + 2.714285714 Reorder the terms: -2.714285714 + 2.714285714 + -2x + x2 = 0 + 2.714285714 Combine like terms: -2.714285714 + 2.714285714 = 0.000000000 0.000000000 + -2x + x2 = 0 + 2.714285714 -2x + x2 = 0 + 2.714285714 Combine like terms: 0 + 2.714285714 = 2.714285714 -2x + x2 = 2.714285714 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 2.714285714 + 1 Reorder the terms: 1 + -2x + x2 = 2.714285714 + 1 Combine like terms: 2.714285714 + 1 = 3.714285714 1 + -2x + x2 = 3.714285714 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.714285714 Calculate the square root of the right side: 1.927248223 Break this problem into two subproblems by setting (x + -1) equal to 1.927248223 and -1.927248223.Subproblem 1
x + -1 = 1.927248223 Simplifying x + -1 = 1.927248223 Reorder the terms: -1 + x = 1.927248223 Solving -1 + x = 1.927248223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.927248223 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.927248223 + 1 x = 1.927248223 + 1 Combine like terms: 1.927248223 + 1 = 2.927248223 x = 2.927248223 Simplifying x = 2.927248223Subproblem 2
x + -1 = -1.927248223 Simplifying x + -1 = -1.927248223 Reorder the terms: -1 + x = -1.927248223 Solving -1 + x = -1.927248223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.927248223 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.927248223 + 1 x = -1.927248223 + 1 Combine like terms: -1.927248223 + 1 = -0.927248223 x = -0.927248223 Simplifying x = -0.927248223Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.927248223, -0.927248223}
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