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Simplifying 5x2 + -4x + -461 = 0 Reorder the terms: -461 + -4x + 5x2 = 0 Solving -461 + -4x + 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'. -92.2 + -0.8x + x2 = 0 Move the constant term to the right: Add '92.2' to each side of the equation. -92.2 + -0.8x + 92.2 + x2 = 0 + 92.2 Reorder the terms: -92.2 + 92.2 + -0.8x + x2 = 0 + 92.2 Combine like terms: -92.2 + 92.2 = 0.0 0.0 + -0.8x + x2 = 0 + 92.2 -0.8x + x2 = 0 + 92.2 Combine like terms: 0 + 92.2 = 92.2 -0.8x + x2 = 92.2 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 92.2 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 92.2 + 0.16 Combine like terms: 92.2 + 0.16 = 92.36 0.16 + -0.8x + x2 = 92.36 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 92.36 Calculate the square root of the right side: 9.610411021 Break this problem into two subproblems by setting (x + -0.4) equal to 9.610411021 and -9.610411021.Subproblem 1
x + -0.4 = 9.610411021 Simplifying x + -0.4 = 9.610411021 Reorder the terms: -0.4 + x = 9.610411021 Solving -0.4 + x = 9.610411021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 9.610411021 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 9.610411021 + 0.4 x = 9.610411021 + 0.4 Combine like terms: 9.610411021 + 0.4 = 10.010411021 x = 10.010411021 Simplifying x = 10.010411021Subproblem 2
x + -0.4 = -9.610411021 Simplifying x + -0.4 = -9.610411021 Reorder the terms: -0.4 + x = -9.610411021 Solving -0.4 + x = -9.610411021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -9.610411021 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -9.610411021 + 0.4 x = -9.610411021 + 0.4 Combine like terms: -9.610411021 + 0.4 = -9.210411021 x = -9.210411021 Simplifying x = -9.210411021Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.010411021, -9.210411021}
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