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Simplifying 7x2 + -19x + 6 = 0 Reorder the terms: 6 + -19x + 7x2 = 0 Solving 6 + -19x + 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'. 0.8571428571 + -2.714285714x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -2.714285714x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -2.714285714x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -2.714285714x + x2 = 0 + -0.8571428571 -2.714285714x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -2.714285714x + x2 = -0.8571428571 The x term is -2.714285714x. Take half its coefficient (-1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. -2.714285714x + 1.841836734 + x2 = -0.8571428571 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = -0.8571428571 + 1.841836734 Combine like terms: -0.8571428571 + 1.841836734 = 0.9846938769 1.841836734 + -2.714285714x + x2 = 0.9846938769 Factor a perfect square on the left side: (x + -1.357142857)(x + -1.357142857) = 0.9846938769 Calculate the square root of the right side: 0.992317427 Break this problem into two subproblems by setting (x + -1.357142857) equal to 0.992317427 and -0.992317427.Subproblem 1
x + -1.357142857 = 0.992317427 Simplifying x + -1.357142857 = 0.992317427 Reorder the terms: -1.357142857 + x = 0.992317427 Solving -1.357142857 + x = 0.992317427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + x = 0.992317427 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 0.992317427 + 1.357142857 x = 0.992317427 + 1.357142857 Combine like terms: 0.992317427 + 1.357142857 = 2.349460284 x = 2.349460284 Simplifying x = 2.349460284Subproblem 2
x + -1.357142857 = -0.992317427 Simplifying x + -1.357142857 = -0.992317427 Reorder the terms: -1.357142857 + x = -0.992317427 Solving -1.357142857 + x = -0.992317427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + x = -0.992317427 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -0.992317427 + 1.357142857 x = -0.992317427 + 1.357142857 Combine like terms: -0.992317427 + 1.357142857 = 0.36482543 x = 0.36482543 Simplifying x = 0.36482543Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.349460284, 0.36482543}
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