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Simplifying x2 * 7 + 19x + 9 = 19 Reorder the terms for easier multiplication: 7x2 + 19x + 9 = 19 Reorder the terms: 9 + 19x + 7x2 = 19 Solving 9 + 19x + 7x2 = 19 Solving for variable 'x'. Reorder the terms: 9 + -19 + 19x + 7x2 = 19 + -19 Combine like terms: 9 + -19 = -10 -10 + 19x + 7x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -10 + 19x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 2.714285714x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 2.714285714x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 2.714285714x + x2 = 0 + 1.428571429 2.714285714x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 2.714285714x + x2 = 1.428571429 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 = 1.428571429 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 1.428571429 + 1.841836734 Combine like terms: 1.428571429 + 1.841836734 = 3.270408163 1.841836734 + 2.714285714x + x2 = 3.270408163 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 3.270408163 Calculate the square root of the right side: 1.808426986 Break this problem into two subproblems by setting (x + 1.357142857) equal to 1.808426986 and -1.808426986.Subproblem 1
x + 1.357142857 = 1.808426986 Simplifying x + 1.357142857 = 1.808426986 Reorder the terms: 1.357142857 + x = 1.808426986 Solving 1.357142857 + x = 1.808426986 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 = 1.808426986 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 1.808426986 + -1.357142857 x = 1.808426986 + -1.357142857 Combine like terms: 1.808426986 + -1.357142857 = 0.451284129 x = 0.451284129 Simplifying x = 0.451284129Subproblem 2
x + 1.357142857 = -1.808426986 Simplifying x + 1.357142857 = -1.808426986 Reorder the terms: 1.357142857 + x = -1.808426986 Solving 1.357142857 + x = -1.808426986 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 = -1.808426986 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -1.808426986 + -1.357142857 x = -1.808426986 + -1.357142857 Combine like terms: -1.808426986 + -1.357142857 = -3.165569843 x = -3.165569843 Simplifying x = -3.165569843Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.451284129, -3.165569843}
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