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Simplifying 7x2 + 19x + -9 = 0 Reorder the terms: -9 + 19x + 7x2 = 0 Solving -9 + 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'. -1.285714286 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 2.714285714x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 2.714285714x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 2.714285714x + x2 = 0 + 1.285714286 2.714285714x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 2.714285714x + x2 = 1.285714286 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 = 1.285714286 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 1.285714286 + 1.841836734 Combine like terms: 1.285714286 + 1.841836734 = 3.12755102 1.841836734 + 2.714285714x + x2 = 3.12755102 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 3.12755102 Calculate the square root of the right side: 1.768488343 Break this problem into two subproblems by setting (x + 1.357142857) equal to 1.768488343 and -1.768488343.Subproblem 1
x + 1.357142857 = 1.768488343 Simplifying x + 1.357142857 = 1.768488343 Reorder the terms: 1.357142857 + x = 1.768488343 Solving 1.357142857 + x = 1.768488343 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 = 1.768488343 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 1.768488343 + -1.357142857 x = 1.768488343 + -1.357142857 Combine like terms: 1.768488343 + -1.357142857 = 0.411345486 x = 0.411345486 Simplifying x = 0.411345486Subproblem 2
x + 1.357142857 = -1.768488343 Simplifying x + 1.357142857 = -1.768488343 Reorder the terms: 1.357142857 + x = -1.768488343 Solving 1.357142857 + x = -1.768488343 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 = -1.768488343 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -1.768488343 + -1.357142857 x = -1.768488343 + -1.357142857 Combine like terms: -1.768488343 + -1.357142857 = -3.1256312 x = -3.1256312 Simplifying x = -3.1256312Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.411345486, -3.1256312}
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