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Simplifying x2 + 19x + 14 = 0 Reorder the terms: 14 + 19x + x2 = 0 Solving 14 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 19x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 19x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 19x + x2 = 0 + -14 19x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 19x + x2 = -14 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -14 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -14 + 90.25 Combine like terms: -14 + 90.25 = 76.25 90.25 + 19x + x2 = 76.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + 9.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + 9.5 = 8.732124598 Simplifying x + 9.5 = 8.732124598 Reorder the terms: 9.5 + x = 8.732124598 Solving 9.5 + x = 8.732124598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 8.732124598 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 8.732124598 + -9.5 x = 8.732124598 + -9.5 Combine like terms: 8.732124598 + -9.5 = -0.767875402 x = -0.767875402 Simplifying x = -0.767875402Subproblem 2
x + 9.5 = -8.732124598 Simplifying x + 9.5 = -8.732124598 Reorder the terms: 9.5 + x = -8.732124598 Solving 9.5 + x = -8.732124598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -8.732124598 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -8.732124598 + -9.5 x = -8.732124598 + -9.5 Combine like terms: -8.732124598 + -9.5 = -18.232124598 x = -18.232124598 Simplifying x = -18.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.767875402, -18.232124598}
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