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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 = 6.714285714 4 + 4x + x2 = 6.714285714 Factor a perfect square on the left side: (x + 2)(x + 2) = 6.714285714 Calculate the square root of the right side: 2.591193878 Break this problem into two subproblems by setting (x + 2) equal to 2.591193878 and -2.591193878.Subproblem 1
x + 2 = 2.591193878 Simplifying x + 2 = 2.591193878 Reorder the terms: 2 + x = 2.591193878 Solving 2 + x = 2.591193878 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 = 2.591193878 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.591193878 + -2 x = 2.591193878 + -2 Combine like terms: 2.591193878 + -2 = 0.591193878 x = 0.591193878 Simplifying x = 0.591193878Subproblem 2
x + 2 = -2.591193878 Simplifying x + 2 = -2.591193878 Reorder the terms: 2 + x = -2.591193878 Solving 2 + x = -2.591193878 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 = -2.591193878 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.591193878 + -2 x = -2.591193878 + -2 Combine like terms: -2.591193878 + -2 = -4.591193878 x = -4.591193878 Simplifying x = -4.591193878Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.591193878, -4.591193878}
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