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Simplifying 7x2 + 19x = 16 Reorder the terms: 19x + 7x2 = 16 Solving 19x + 7x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 19x + 7x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 19x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 2.714285714x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 2.714285714x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 2.714285714x + x2 = 0 + 2.285714286 2.714285714x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 2.714285714x + x2 = 2.285714286 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 = 2.285714286 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 2.285714286 + 1.841836734 Combine like terms: 2.285714286 + 1.841836734 = 4.12755102 1.841836734 + 2.714285714x + x2 = 4.12755102 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 4.12755102 Calculate the square root of the right side: 2.031637522 Break this problem into two subproblems by setting (x + 1.357142857) equal to 2.031637522 and -2.031637522.Subproblem 1
x + 1.357142857 = 2.031637522 Simplifying x + 1.357142857 = 2.031637522 Reorder the terms: 1.357142857 + x = 2.031637522 Solving 1.357142857 + x = 2.031637522 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 = 2.031637522 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 2.031637522 + -1.357142857 x = 2.031637522 + -1.357142857 Combine like terms: 2.031637522 + -1.357142857 = 0.674494665 x = 0.674494665 Simplifying x = 0.674494665Subproblem 2
x + 1.357142857 = -2.031637522 Simplifying x + 1.357142857 = -2.031637522 Reorder the terms: 1.357142857 + x = -2.031637522 Solving 1.357142857 + x = -2.031637522 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 = -2.031637522 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -2.031637522 + -1.357142857 x = -2.031637522 + -1.357142857 Combine like terms: -2.031637522 + -1.357142857 = -3.388780379 x = -3.388780379 Simplifying x = -3.388780379Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.674494665, -3.388780379}
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