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Simplifying 14.2 + 8x + x2 = 0 Solving 14.2 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14.2' to each side of the equation. 14.2 + 8x + -14.2 + x2 = 0 + -14.2 Reorder the terms: 14.2 + -14.2 + 8x + x2 = 0 + -14.2 Combine like terms: 14.2 + -14.2 = 0.0 0.0 + 8x + x2 = 0 + -14.2 8x + x2 = 0 + -14.2 Combine like terms: 0 + -14.2 = -14.2 8x + x2 = -14.2 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -14.2 + 16 Reorder the terms: 16 + 8x + x2 = -14.2 + 16 Combine like terms: -14.2 + 16 = 1.8 16 + 8x + x2 = 1.8 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.8 Calculate the square root of the right side: 1.341640787 Break this problem into two subproblems by setting (x + 4) equal to 1.341640787 and -1.341640787.Subproblem 1
x + 4 = 1.341640787 Simplifying x + 4 = 1.341640787 Reorder the terms: 4 + x = 1.341640787 Solving 4 + x = 1.341640787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 1.341640787 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.341640787 + -4 x = 1.341640787 + -4 Combine like terms: 1.341640787 + -4 = -2.658359213 x = -2.658359213 Simplifying x = -2.658359213Subproblem 2
x + 4 = -1.341640787 Simplifying x + 4 = -1.341640787 Reorder the terms: 4 + x = -1.341640787 Solving 4 + x = -1.341640787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -1.341640787 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.341640787 + -4 x = -1.341640787 + -4 Combine like terms: -1.341640787 + -4 = -5.341640787 x = -5.341640787 Simplifying x = -5.341640787Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.658359213, -5.341640787}
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