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Simplifying 7x2 + 12x + 2 = 0 Reorder the terms: 2 + 12x + 7x2 = 0 Solving 2 + 12x + 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'. 0.2857142857 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 1.714285714x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 1.714285714x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 1.714285714x + x2 = 0 + -0.2857142857 1.714285714x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 1.714285714x + x2 = -0.2857142857 The x term is 1.714285714x. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x + 0.7346938773 + x2 = -0.2857142857 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = -0.2857142857 + 0.7346938773 Combine like terms: -0.2857142857 + 0.7346938773 = 0.4489795916 0.7346938773 + 1.714285714x + x2 = 0.4489795916 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 0.4489795916 Calculate the square root of the right side: 0.670059394 Break this problem into two subproblems by setting (x + 0.857142857) equal to 0.670059394 and -0.670059394.Subproblem 1
x + 0.857142857 = 0.670059394 Simplifying x + 0.857142857 = 0.670059394 Reorder the terms: 0.857142857 + x = 0.670059394 Solving 0.857142857 + x = 0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = 0.670059394 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 0.670059394 + -0.857142857 x = 0.670059394 + -0.857142857 Combine like terms: 0.670059394 + -0.857142857 = -0.187083463 x = -0.187083463 Simplifying x = -0.187083463Subproblem 2
x + 0.857142857 = -0.670059394 Simplifying x + 0.857142857 = -0.670059394 Reorder the terms: 0.857142857 + x = -0.670059394 Solving 0.857142857 + x = -0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = -0.670059394 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -0.670059394 + -0.857142857 x = -0.670059394 + -0.857142857 Combine like terms: -0.670059394 + -0.857142857 = -1.527202251 x = -1.527202251 Simplifying x = -1.527202251Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.187083463, -1.527202251}
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