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Simplifying 7x2 + 15x + 6 = 0 Reorder the terms: 6 + 15x + 7x2 = 0 Solving 6 + 15x + 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'. 0.8571428571 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 2.142857143x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 2.142857143x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 2.142857143x + x2 = 0 + -0.8571428571 2.142857143x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 2.142857143x + x2 = -0.8571428571 The x term is 2.142857143x. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143x + 1.147959185 + x2 = -0.8571428571 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = -0.8571428571 + 1.147959185 Combine like terms: -0.8571428571 + 1.147959185 = 0.2908163279 1.147959185 + 2.142857143x + x2 = 0.2908163279 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 0.2908163279 Calculate the square root of the right side: 0.53927389 Break this problem into two subproblems by setting (x + 1.071428572) equal to 0.53927389 and -0.53927389.Subproblem 1
x + 1.071428572 = 0.53927389 Simplifying x + 1.071428572 = 0.53927389 Reorder the terms: 1.071428572 + x = 0.53927389 Solving 1.071428572 + x = 0.53927389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = 0.53927389 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 0.53927389 + -1.071428572 x = 0.53927389 + -1.071428572 Combine like terms: 0.53927389 + -1.071428572 = -0.532154682 x = -0.532154682 Simplifying x = -0.532154682Subproblem 2
x + 1.071428572 = -0.53927389 Simplifying x + 1.071428572 = -0.53927389 Reorder the terms: 1.071428572 + x = -0.53927389 Solving 1.071428572 + x = -0.53927389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = -0.53927389 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -0.53927389 + -1.071428572 x = -0.53927389 + -1.071428572 Combine like terms: -0.53927389 + -1.071428572 = -1.610702462 x = -1.610702462 Simplifying x = -1.610702462Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.532154682, -1.610702462}
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