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Simplifying 5x2 + -41x + 30 = 0 Reorder the terms: 30 + -41x + 5x2 = 0 Solving 30 + -41x + 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'. 6 + -8.2x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8.2x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -8.2x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8.2x + x2 = 0 + -6 -8.2x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8.2x + x2 = -6 The x term is -8.2x. Take half its coefficient (-4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. -8.2x + 16.81 + x2 = -6 + 16.81 Reorder the terms: 16.81 + -8.2x + x2 = -6 + 16.81 Combine like terms: -6 + 16.81 = 10.81 16.81 + -8.2x + x2 = 10.81 Factor a perfect square on the left side: (x + -4.1)(x + -4.1) = 10.81 Calculate the square root of the right side: 3.287856445 Break this problem into two subproblems by setting (x + -4.1) equal to 3.287856445 and -3.287856445.Subproblem 1
x + -4.1 = 3.287856445 Simplifying x + -4.1 = 3.287856445 Reorder the terms: -4.1 + x = 3.287856445 Solving -4.1 + x = 3.287856445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = 3.287856445 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = 3.287856445 + 4.1 x = 3.287856445 + 4.1 Combine like terms: 3.287856445 + 4.1 = 7.387856445 x = 7.387856445 Simplifying x = 7.387856445Subproblem 2
x + -4.1 = -3.287856445 Simplifying x + -4.1 = -3.287856445 Reorder the terms: -4.1 + x = -3.287856445 Solving -4.1 + x = -3.287856445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = -3.287856445 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = -3.287856445 + 4.1 x = -3.287856445 + 4.1 Combine like terms: -3.287856445 + 4.1 = 0.812143555 x = 0.812143555 Simplifying x = 0.812143555Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.387856445, 0.812143555}
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