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Simplifying 7x2 + 28x + 19 = 0 Reorder the terms: 19 + 28x + 7x2 = 0 Solving 19 + 28x + 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'. 2.714285714 + 4x + x2 = 0 Move the constant term to the right: Add '-2.714285714' to each side of the equation. 2.714285714 + 4x + -2.714285714 + x2 = 0 + -2.714285714 Reorder the terms: 2.714285714 + -2.714285714 + 4x + x2 = 0 + -2.714285714 Combine like terms: 2.714285714 + -2.714285714 = 0.000000000 0.000000000 + 4x + x2 = 0 + -2.714285714 4x + x2 = 0 + -2.714285714 Combine like terms: 0 + -2.714285714 = -2.714285714 4x + x2 = -2.714285714 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2.714285714 + 4 Reorder the terms: 4 + 4x + x2 = -2.714285714 + 4 Combine like terms: -2.714285714 + 4 = 1.285714286 4 + 4x + x2 = 1.285714286 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.285714286 Calculate the square root of the right side: 1.133893419 Break this problem into two subproblems by setting (x + 2) equal to 1.133893419 and -1.133893419.Subproblem 1
x + 2 = 1.133893419 Simplifying x + 2 = 1.133893419 Reorder the terms: 2 + x = 1.133893419 Solving 2 + x = 1.133893419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.133893419 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.133893419 + -2 x = 1.133893419 + -2 Combine like terms: 1.133893419 + -2 = -0.866106581 x = -0.866106581 Simplifying x = -0.866106581Subproblem 2
x + 2 = -1.133893419 Simplifying x + 2 = -1.133893419 Reorder the terms: 2 + x = -1.133893419 Solving 2 + x = -1.133893419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.133893419 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.133893419 + -2 x = -1.133893419 + -2 Combine like terms: -1.133893419 + -2 = -3.133893419 x = -3.133893419 Simplifying x = -3.133893419Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.866106581, -3.133893419}
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