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Simplifying -19x + 7x2 = 19 Solving -19x + 7x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + -19x + 7x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -19x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.714285714 + -2.714285714x + x2 = 0 Move the constant term to the right: Add '2.714285714' to each side of the equation. -2.714285714 + -2.714285714x + 2.714285714 + x2 = 0 + 2.714285714 Reorder the terms: -2.714285714 + 2.714285714 + -2.714285714x + x2 = 0 + 2.714285714 Combine like terms: -2.714285714 + 2.714285714 = 0.000000000 0.000000000 + -2.714285714x + x2 = 0 + 2.714285714 -2.714285714x + x2 = 0 + 2.714285714 Combine like terms: 0 + 2.714285714 = 2.714285714 -2.714285714x + x2 = 2.714285714 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 = 2.714285714 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = 2.714285714 + 1.841836734 Combine like terms: 2.714285714 + 1.841836734 = 4.556122448 1.841836734 + -2.714285714x + x2 = 4.556122448 Factor a perfect square on the left side: (x + -1.357142857)(x + -1.357142857) = 4.556122448 Calculate the square root of the right side: 2.134507542 Break this problem into two subproblems by setting (x + -1.357142857) equal to 2.134507542 and -2.134507542.Subproblem 1
x + -1.357142857 = 2.134507542 Simplifying x + -1.357142857 = 2.134507542 Reorder the terms: -1.357142857 + x = 2.134507542 Solving -1.357142857 + x = 2.134507542 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 = 2.134507542 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 2.134507542 + 1.357142857 x = 2.134507542 + 1.357142857 Combine like terms: 2.134507542 + 1.357142857 = 3.491650399 x = 3.491650399 Simplifying x = 3.491650399Subproblem 2
x + -1.357142857 = -2.134507542 Simplifying x + -1.357142857 = -2.134507542 Reorder the terms: -1.357142857 + x = -2.134507542 Solving -1.357142857 + x = -2.134507542 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 = -2.134507542 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -2.134507542 + 1.357142857 x = -2.134507542 + 1.357142857 Combine like terms: -2.134507542 + 1.357142857 = -0.777364685 x = -0.777364685 Simplifying x = -0.777364685Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.491650399, -0.777364685}
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