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Simplifying 8x2 + 65x + 14 = 0 Reorder the terms: 14 + 65x + 8x2 = 0 Solving 14 + 65x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.75 + 8.125x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 8.125x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 8.125x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 8.125x + x2 = 0 + -1.75 8.125x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 8.125x + x2 = -1.75 The x term is 8.125x. Take half its coefficient (4.0625). Square it (16.50390625) and add it to both sides. Add '16.50390625' to each side of the equation. 8.125x + 16.50390625 + x2 = -1.75 + 16.50390625 Reorder the terms: 16.50390625 + 8.125x + x2 = -1.75 + 16.50390625 Combine like terms: -1.75 + 16.50390625 = 14.75390625 16.50390625 + 8.125x + x2 = 14.75390625 Factor a perfect square on the left side: (x + 4.0625)(x + 4.0625) = 14.75390625 Calculate the square root of the right side: 3.841081391 Break this problem into two subproblems by setting (x + 4.0625) equal to 3.841081391 and -3.841081391.Subproblem 1
x + 4.0625 = 3.841081391 Simplifying x + 4.0625 = 3.841081391 Reorder the terms: 4.0625 + x = 3.841081391 Solving 4.0625 + x = 3.841081391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.0625' to each side of the equation. 4.0625 + -4.0625 + x = 3.841081391 + -4.0625 Combine like terms: 4.0625 + -4.0625 = 0.0000 0.0000 + x = 3.841081391 + -4.0625 x = 3.841081391 + -4.0625 Combine like terms: 3.841081391 + -4.0625 = -0.221418609 x = -0.221418609 Simplifying x = -0.221418609Subproblem 2
x + 4.0625 = -3.841081391 Simplifying x + 4.0625 = -3.841081391 Reorder the terms: 4.0625 + x = -3.841081391 Solving 4.0625 + x = -3.841081391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.0625' to each side of the equation. 4.0625 + -4.0625 + x = -3.841081391 + -4.0625 Combine like terms: 4.0625 + -4.0625 = 0.0000 0.0000 + x = -3.841081391 + -4.0625 x = -3.841081391 + -4.0625 Combine like terms: -3.841081391 + -4.0625 = -7.903581391 x = -7.903581391 Simplifying x = -7.903581391Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.221418609, -7.903581391}
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