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Simplifying 5x2 + -38x + -8 = 0 Reorder the terms: -8 + -38x + 5x2 = 0 Solving -8 + -38x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -7.6x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -7.6x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -7.6x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -7.6x + x2 = 0 + 1.6 -7.6x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -7.6x + x2 = 1.6 The x term is -7.6x. Take half its coefficient (-3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. -7.6x + 14.44 + x2 = 1.6 + 14.44 Reorder the terms: 14.44 + -7.6x + x2 = 1.6 + 14.44 Combine like terms: 1.6 + 14.44 = 16.04 14.44 + -7.6x + x2 = 16.04 Factor a perfect square on the left side: (x + -3.8)(x + -3.8) = 16.04 Calculate the square root of the right side: 4.004996879 Break this problem into two subproblems by setting (x + -3.8) equal to 4.004996879 and -4.004996879.Subproblem 1
x + -3.8 = 4.004996879 Simplifying x + -3.8 = 4.004996879 Reorder the terms: -3.8 + x = 4.004996879 Solving -3.8 + x = 4.004996879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 4.004996879 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 4.004996879 + 3.8 x = 4.004996879 + 3.8 Combine like terms: 4.004996879 + 3.8 = 7.804996879 x = 7.804996879 Simplifying x = 7.804996879Subproblem 2
x + -3.8 = -4.004996879 Simplifying x + -3.8 = -4.004996879 Reorder the terms: -3.8 + x = -4.004996879 Solving -3.8 + x = -4.004996879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = -4.004996879 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = -4.004996879 + 3.8 x = -4.004996879 + 3.8 Combine like terms: -4.004996879 + 3.8 = -0.204996879 x = -0.204996879 Simplifying x = -0.204996879Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.804996879, -0.204996879}
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