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Simplifying 7x2 + -29x + -42 = 0 Reorder the terms: -42 + -29x + 7x2 = 0 Solving -42 + -29x + 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'. -6 + -4.142857143x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -4.142857143x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -4.142857143x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4.142857143x + x2 = 0 + 6 -4.142857143x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4.142857143x + x2 = 6 The x term is -4.142857143x. Take half its coefficient (-2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. -4.142857143x + 4.290816329 + x2 = 6 + 4.290816329 Reorder the terms: 4.290816329 + -4.142857143x + x2 = 6 + 4.290816329 Combine like terms: 6 + 4.290816329 = 10.290816329 4.290816329 + -4.142857143x + x2 = 10.290816329 Factor a perfect square on the left side: (x + -2.071428572)(x + -2.071428572) = 10.290816329 Calculate the square root of the right side: 3.207930225 Break this problem into two subproblems by setting (x + -2.071428572) equal to 3.207930225 and -3.207930225.Subproblem 1
x + -2.071428572 = 3.207930225 Simplifying x + -2.071428572 = 3.207930225 Reorder the terms: -2.071428572 + x = 3.207930225 Solving -2.071428572 + x = 3.207930225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = 3.207930225 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = 3.207930225 + 2.071428572 x = 3.207930225 + 2.071428572 Combine like terms: 3.207930225 + 2.071428572 = 5.279358797 x = 5.279358797 Simplifying x = 5.279358797Subproblem 2
x + -2.071428572 = -3.207930225 Simplifying x + -2.071428572 = -3.207930225 Reorder the terms: -2.071428572 + x = -3.207930225 Solving -2.071428572 + x = -3.207930225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = -3.207930225 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = -3.207930225 + 2.071428572 x = -3.207930225 + 2.071428572 Combine like terms: -3.207930225 + 2.071428572 = -1.136501653 x = -1.136501653 Simplifying x = -1.136501653Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.279358797, -1.136501653}
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