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Simplifying 35x2 + -56x + -9 = 0 Reorder the terms: -9 + -56x + 35x2 = 0 Solving -9 + -56x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.2571428571 + -1.6x + x2 = 0 Move the constant term to the right: Add '0.2571428571' to each side of the equation. -0.2571428571 + -1.6x + 0.2571428571 + x2 = 0 + 0.2571428571 Reorder the terms: -0.2571428571 + 0.2571428571 + -1.6x + x2 = 0 + 0.2571428571 Combine like terms: -0.2571428571 + 0.2571428571 = 0.0000000000 0.0000000000 + -1.6x + x2 = 0 + 0.2571428571 -1.6x + x2 = 0 + 0.2571428571 Combine like terms: 0 + 0.2571428571 = 0.2571428571 -1.6x + x2 = 0.2571428571 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 0.2571428571 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 0.2571428571 + 0.64 Combine like terms: 0.2571428571 + 0.64 = 0.8971428571 0.64 + -1.6x + x2 = 0.8971428571 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.8971428571 Calculate the square root of the right side: 0.947176255 Break this problem into two subproblems by setting (x + -0.8) equal to 0.947176255 and -0.947176255.Subproblem 1
x + -0.8 = 0.947176255 Simplifying x + -0.8 = 0.947176255 Reorder the terms: -0.8 + x = 0.947176255 Solving -0.8 + x = 0.947176255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.947176255 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.947176255 + 0.8 x = 0.947176255 + 0.8 Combine like terms: 0.947176255 + 0.8 = 1.747176255 x = 1.747176255 Simplifying x = 1.747176255Subproblem 2
x + -0.8 = -0.947176255 Simplifying x + -0.8 = -0.947176255 Reorder the terms: -0.8 + x = -0.947176255 Solving -0.8 + x = -0.947176255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -0.947176255 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.947176255 + 0.8 x = -0.947176255 + 0.8 Combine like terms: -0.947176255 + 0.8 = -0.147176255 x = -0.147176255 Simplifying x = -0.147176255Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.747176255, -0.147176255}
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