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Simplifying 7x2 + -19x + 4 = 0 Reorder the terms: 4 + -19x + 7x2 = 0 Solving 4 + -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'. 0.5714285714 + -2.714285714x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -2.714285714x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -2.714285714x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -2.714285714x + x2 = 0 + -0.5714285714 -2.714285714x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -2.714285714x + x2 = -0.5714285714 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 = -0.5714285714 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = -0.5714285714 + 1.841836734 Combine like terms: -0.5714285714 + 1.841836734 = 1.2704081626 1.841836734 + -2.714285714x + x2 = 1.2704081626 Factor a perfect square on the left side: (x + -1.357142857)(x + -1.357142857) = 1.2704081626 Calculate the square root of the right side: 1.127123845 Break this problem into two subproblems by setting (x + -1.357142857) equal to 1.127123845 and -1.127123845.Subproblem 1
x + -1.357142857 = 1.127123845 Simplifying x + -1.357142857 = 1.127123845 Reorder the terms: -1.357142857 + x = 1.127123845 Solving -1.357142857 + x = 1.127123845 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 = 1.127123845 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 1.127123845 + 1.357142857 x = 1.127123845 + 1.357142857 Combine like terms: 1.127123845 + 1.357142857 = 2.484266702 x = 2.484266702 Simplifying x = 2.484266702Subproblem 2
x + -1.357142857 = -1.127123845 Simplifying x + -1.357142857 = -1.127123845 Reorder the terms: -1.357142857 + x = -1.127123845 Solving -1.357142857 + x = -1.127123845 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 = -1.127123845 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -1.127123845 + 1.357142857 x = -1.127123845 + 1.357142857 Combine like terms: -1.127123845 + 1.357142857 = 0.230019012 x = 0.230019012 Simplifying x = 0.230019012Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.484266702, 0.230019012}
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