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Simplifying 15x2 + 6x + -28 = 0 Reorder the terms: -28 + 6x + 15x2 = 0 Solving -28 + 6x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.866666667 + 0.4x + x2 = 0 Move the constant term to the right: Add '1.866666667' to each side of the equation. -1.866666667 + 0.4x + 1.866666667 + x2 = 0 + 1.866666667 Reorder the terms: -1.866666667 + 1.866666667 + 0.4x + x2 = 0 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + 0.4x + x2 = 0 + 1.866666667 0.4x + x2 = 0 + 1.866666667 Combine like terms: 0 + 1.866666667 = 1.866666667 0.4x + x2 = 1.866666667 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 1.866666667 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 1.866666667 + 0.04 Combine like terms: 1.866666667 + 0.04 = 1.906666667 0.04 + 0.4x + x2 = 1.906666667 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 1.906666667 Calculate the square root of the right side: 1.380821012 Break this problem into two subproblems by setting (x + 0.2) equal to 1.380821012 and -1.380821012.Subproblem 1
x + 0.2 = 1.380821012 Simplifying x + 0.2 = 1.380821012 Reorder the terms: 0.2 + x = 1.380821012 Solving 0.2 + x = 1.380821012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.380821012 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.380821012 + -0.2 x = 1.380821012 + -0.2 Combine like terms: 1.380821012 + -0.2 = 1.180821012 x = 1.180821012 Simplifying x = 1.180821012Subproblem 2
x + 0.2 = -1.380821012 Simplifying x + 0.2 = -1.380821012 Reorder the terms: 0.2 + x = -1.380821012 Solving 0.2 + x = -1.380821012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.380821012 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.380821012 + -0.2 x = -1.380821012 + -0.2 Combine like terms: -1.380821012 + -0.2 = -1.580821012 x = -1.580821012 Simplifying x = -1.580821012Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.180821012, -1.580821012}
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