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Simplifying 7x2 + 34x + 5 = 0 Reorder the terms: 5 + 34x + 7x2 = 0 Solving 5 + 34x + 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'. 0.7142857143 + 4.857142857x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + 4.857142857x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + 4.857142857x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + 4.857142857x + x2 = 0 + -0.7142857143 4.857142857x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 4.857142857x + x2 = -0.7142857143 The x term is 4.857142857x. Take half its coefficient (2.428571429). Square it (5.897959186) and add it to both sides. Add '5.897959186' to each side of the equation. 4.857142857x + 5.897959186 + x2 = -0.7142857143 + 5.897959186 Reorder the terms: 5.897959186 + 4.857142857x + x2 = -0.7142857143 + 5.897959186 Combine like terms: -0.7142857143 + 5.897959186 = 5.1836734717 5.897959186 + 4.857142857x + x2 = 5.1836734717 Factor a perfect square on the left side: (x + 2.428571429)(x + 2.428571429) = 5.1836734717 Calculate the square root of the right side: 2.276768208 Break this problem into two subproblems by setting (x + 2.428571429) equal to 2.276768208 and -2.276768208.Subproblem 1
x + 2.428571429 = 2.276768208 Simplifying x + 2.428571429 = 2.276768208 Reorder the terms: 2.428571429 + x = 2.276768208 Solving 2.428571429 + x = 2.276768208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.428571429' to each side of the equation. 2.428571429 + -2.428571429 + x = 2.276768208 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + x = 2.276768208 + -2.428571429 x = 2.276768208 + -2.428571429 Combine like terms: 2.276768208 + -2.428571429 = -0.151803221 x = -0.151803221 Simplifying x = -0.151803221Subproblem 2
x + 2.428571429 = -2.276768208 Simplifying x + 2.428571429 = -2.276768208 Reorder the terms: 2.428571429 + x = -2.276768208 Solving 2.428571429 + x = -2.276768208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.428571429' to each side of the equation. 2.428571429 + -2.428571429 + x = -2.276768208 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + x = -2.276768208 + -2.428571429 x = -2.276768208 + -2.428571429 Combine like terms: -2.276768208 + -2.428571429 = -4.705339637 x = -4.705339637 Simplifying x = -4.705339637Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.151803221, -4.705339637}
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