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Simplifying -7x2 + -43x + -18 = 0 Reorder the terms: -18 + -43x + -7x2 = 0 Solving -18 + -43x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(18 + 43x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(18 + 43x + 7x2)' equal to zero and attempt to solve: Simplifying 18 + 43x + 7x2 = 0 Solving 18 + 43x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.571428571 + 6.142857143x + x2 = 0 Move the constant term to the right: Add '-2.571428571' to each side of the equation. 2.571428571 + 6.142857143x + -2.571428571 + x2 = 0 + -2.571428571 Reorder the terms: 2.571428571 + -2.571428571 + 6.142857143x + x2 = 0 + -2.571428571 Combine like terms: 2.571428571 + -2.571428571 = 0.000000000 0.000000000 + 6.142857143x + x2 = 0 + -2.571428571 6.142857143x + x2 = 0 + -2.571428571 Combine like terms: 0 + -2.571428571 = -2.571428571 6.142857143x + x2 = -2.571428571 The x term is 6.142857143x. Take half its coefficient (3.071428572). Square it (9.433673473) and add it to both sides. Add '9.433673473' to each side of the equation. 6.142857143x + 9.433673473 + x2 = -2.571428571 + 9.433673473 Reorder the terms: 9.433673473 + 6.142857143x + x2 = -2.571428571 + 9.433673473 Combine like terms: -2.571428571 + 9.433673473 = 6.862244902 9.433673473 + 6.142857143x + x2 = 6.862244902 Factor a perfect square on the left side: (x + 3.071428572)(x + 3.071428572) = 6.862244902 Calculate the square root of the right side: 2.619588689 Break this problem into two subproblems by setting (x + 3.071428572) equal to 2.619588689 and -2.619588689.Subproblem 1
x + 3.071428572 = 2.619588689 Simplifying x + 3.071428572 = 2.619588689 Reorder the terms: 3.071428572 + x = 2.619588689 Solving 3.071428572 + x = 2.619588689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.071428572' to each side of the equation. 3.071428572 + -3.071428572 + x = 2.619588689 + -3.071428572 Combine like terms: 3.071428572 + -3.071428572 = 0.000000000 0.000000000 + x = 2.619588689 + -3.071428572 x = 2.619588689 + -3.071428572 Combine like terms: 2.619588689 + -3.071428572 = -0.451839883 x = -0.451839883 Simplifying x = -0.451839883Subproblem 2
x + 3.071428572 = -2.619588689 Simplifying x + 3.071428572 = -2.619588689 Reorder the terms: 3.071428572 + x = -2.619588689 Solving 3.071428572 + x = -2.619588689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.071428572' to each side of the equation. 3.071428572 + -3.071428572 + x = -2.619588689 + -3.071428572 Combine like terms: 3.071428572 + -3.071428572 = 0.000000000 0.000000000 + x = -2.619588689 + -3.071428572 x = -2.619588689 + -3.071428572 Combine like terms: -2.619588689 + -3.071428572 = -5.691017261 x = -5.691017261 Simplifying x = -5.691017261Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.451839883, -5.691017261}Solution
x = {-0.451839883, -5.691017261}
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