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Simplifying 7x2 + 38x + 34 = 0 Reorder the terms: 34 + 38x + 7x2 = 0 Solving 34 + 38x + 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'. 4.857142857 + 5.428571429x + x2 = 0 Move the constant term to the right: Add '-4.857142857' to each side of the equation. 4.857142857 + 5.428571429x + -4.857142857 + x2 = 0 + -4.857142857 Reorder the terms: 4.857142857 + -4.857142857 + 5.428571429x + x2 = 0 + -4.857142857 Combine like terms: 4.857142857 + -4.857142857 = 0.000000000 0.000000000 + 5.428571429x + x2 = 0 + -4.857142857 5.428571429x + x2 = 0 + -4.857142857 Combine like terms: 0 + -4.857142857 = -4.857142857 5.428571429x + x2 = -4.857142857 The x term is 5.428571429x. Take half its coefficient (2.714285715). Square it (7.367346943) and add it to both sides. Add '7.367346943' to each side of the equation. 5.428571429x + 7.367346943 + x2 = -4.857142857 + 7.367346943 Reorder the terms: 7.367346943 + 5.428571429x + x2 = -4.857142857 + 7.367346943 Combine like terms: -4.857142857 + 7.367346943 = 2.510204086 7.367346943 + 5.428571429x + x2 = 2.510204086 Factor a perfect square on the left side: (x + 2.714285715)(x + 2.714285715) = 2.510204086 Calculate the square root of the right side: 1.584362359 Break this problem into two subproblems by setting (x + 2.714285715) equal to 1.584362359 and -1.584362359.Subproblem 1
x + 2.714285715 = 1.584362359 Simplifying x + 2.714285715 = 1.584362359 Reorder the terms: 2.714285715 + x = 1.584362359 Solving 2.714285715 + x = 1.584362359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.714285715' to each side of the equation. 2.714285715 + -2.714285715 + x = 1.584362359 + -2.714285715 Combine like terms: 2.714285715 + -2.714285715 = 0.000000000 0.000000000 + x = 1.584362359 + -2.714285715 x = 1.584362359 + -2.714285715 Combine like terms: 1.584362359 + -2.714285715 = -1.129923356 x = -1.129923356 Simplifying x = -1.129923356Subproblem 2
x + 2.714285715 = -1.584362359 Simplifying x + 2.714285715 = -1.584362359 Reorder the terms: 2.714285715 + x = -1.584362359 Solving 2.714285715 + x = -1.584362359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.714285715' to each side of the equation. 2.714285715 + -2.714285715 + x = -1.584362359 + -2.714285715 Combine like terms: 2.714285715 + -2.714285715 = 0.000000000 0.000000000 + x = -1.584362359 + -2.714285715 x = -1.584362359 + -2.714285715 Combine like terms: -1.584362359 + -2.714285715 = -4.298648074 x = -4.298648074 Simplifying x = -4.298648074Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.129923356, -4.298648074}
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