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Simplifying 7x2 + -19x + -20 = 0 Reorder the terms: -20 + -19x + 7x2 = 0 Solving -20 + -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'. -2.857142857 + -2.714285714x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -2.714285714x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -2.714285714x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -2.714285714x + x2 = 0 + 2.857142857 -2.714285714x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -2.714285714x + x2 = 2.857142857 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 = 2.857142857 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = 2.857142857 + 1.841836734 Combine like terms: 2.857142857 + 1.841836734 = 4.698979591 1.841836734 + -2.714285714x + x2 = 4.698979591 Factor a perfect square on the left side: (x + -1.357142857)(x + -1.357142857) = 4.698979591 Calculate the square root of the right side: 2.167712986 Break this problem into two subproblems by setting (x + -1.357142857) equal to 2.167712986 and -2.167712986.Subproblem 1
x + -1.357142857 = 2.167712986 Simplifying x + -1.357142857 = 2.167712986 Reorder the terms: -1.357142857 + x = 2.167712986 Solving -1.357142857 + x = 2.167712986 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 = 2.167712986 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 2.167712986 + 1.357142857 x = 2.167712986 + 1.357142857 Combine like terms: 2.167712986 + 1.357142857 = 3.524855843 x = 3.524855843 Simplifying x = 3.524855843Subproblem 2
x + -1.357142857 = -2.167712986 Simplifying x + -1.357142857 = -2.167712986 Reorder the terms: -1.357142857 + x = -2.167712986 Solving -1.357142857 + x = -2.167712986 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 = -2.167712986 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -2.167712986 + 1.357142857 x = -2.167712986 + 1.357142857 Combine like terms: -2.167712986 + 1.357142857 = -0.810570129 x = -0.810570129 Simplifying x = -0.810570129Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.524855843, -0.810570129}
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