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Simplifying 7x2 + -6x + -19 = 0 Reorder the terms: -19 + -6x + 7x2 = 0 Solving -19 + -6x + 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 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '2.714285714' to each side of the equation. -2.714285714 + -0.8571428571x + 2.714285714 + x2 = 0 + 2.714285714 Reorder the terms: -2.714285714 + 2.714285714 + -0.8571428571x + x2 = 0 + 2.714285714 Combine like terms: -2.714285714 + 2.714285714 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + 2.714285714 -0.8571428571x + x2 = 0 + 2.714285714 Combine like terms: 0 + 2.714285714 = 2.714285714 -0.8571428571x + x2 = 2.714285714 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 2.714285714 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 2.714285714 + 0.1836734694 Combine like terms: 2.714285714 + 0.1836734694 = 2.8979591834 0.1836734694 + -0.8571428571x + x2 = 2.8979591834 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 2.8979591834 Calculate the square root of the right side: 1.702339327 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.702339327 and -1.702339327.Subproblem 1
x + -0.4285714286 = 1.702339327 Simplifying x + -0.4285714286 = 1.702339327 Reorder the terms: -0.4285714286 + x = 1.702339327 Solving -0.4285714286 + x = 1.702339327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 1.702339327 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.702339327 + 0.4285714286 x = 1.702339327 + 0.4285714286 Combine like terms: 1.702339327 + 0.4285714286 = 2.1309107556 x = 2.1309107556 Simplifying x = 2.1309107556Subproblem 2
x + -0.4285714286 = -1.702339327 Simplifying x + -0.4285714286 = -1.702339327 Reorder the terms: -0.4285714286 + x = -1.702339327 Solving -0.4285714286 + x = -1.702339327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -1.702339327 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.702339327 + 0.4285714286 x = -1.702339327 + 0.4285714286 Combine like terms: -1.702339327 + 0.4285714286 = -1.2737678984 x = -1.2737678984 Simplifying x = -1.2737678984Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1309107556, -1.2737678984}
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