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Simplifying 7x2 + 19x + -21 = 0 Reorder the terms: -21 + 19x + 7x2 = 0 Solving -21 + 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'. -3 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.714285714x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.714285714x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.714285714x + x2 = 0 + 3 2.714285714x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.714285714x + x2 = 3 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 = 3 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 3 + 1.841836734 Combine like terms: 3 + 1.841836734 = 4.841836734 1.841836734 + 2.714285714x + x2 = 4.841836734 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 4.841836734 Calculate the square root of the right side: 2.2004174 Break this problem into two subproblems by setting (x + 1.357142857) equal to 2.2004174 and -2.2004174.Subproblem 1
x + 1.357142857 = 2.2004174 Simplifying x + 1.357142857 = 2.2004174 Reorder the terms: 1.357142857 + x = 2.2004174 Solving 1.357142857 + x = 2.2004174 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 = 2.2004174 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 2.2004174 + -1.357142857 x = 2.2004174 + -1.357142857 Combine like terms: 2.2004174 + -1.357142857 = 0.843274543 x = 0.843274543 Simplifying x = 0.843274543Subproblem 2
x + 1.357142857 = -2.2004174 Simplifying x + 1.357142857 = -2.2004174 Reorder the terms: 1.357142857 + x = -2.2004174 Solving 1.357142857 + x = -2.2004174 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 = -2.2004174 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -2.2004174 + -1.357142857 x = -2.2004174 + -1.357142857 Combine like terms: -2.2004174 + -1.357142857 = -3.557560257 x = -3.557560257 Simplifying x = -3.557560257Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.843274543, -3.557560257}
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