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Simplifying 5x2 + -55x + 148 = 0 Reorder the terms: 148 + -55x + 5x2 = 0 Solving 148 + -55x + 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'. 29.6 + -11x + x2 = 0 Move the constant term to the right: Add '-29.6' to each side of the equation. 29.6 + -11x + -29.6 + x2 = 0 + -29.6 Reorder the terms: 29.6 + -29.6 + -11x + x2 = 0 + -29.6 Combine like terms: 29.6 + -29.6 = 0.0 0.0 + -11x + x2 = 0 + -29.6 -11x + x2 = 0 + -29.6 Combine like terms: 0 + -29.6 = -29.6 -11x + x2 = -29.6 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -29.6 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -29.6 + 30.25 Combine like terms: -29.6 + 30.25 = 0.65 30.25 + -11x + x2 = 0.65 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (x + -5.5) equal to 0.806225775 and -0.806225775.Subproblem 1
x + -5.5 = 0.806225775 Simplifying x + -5.5 = 0.806225775 Reorder the terms: -5.5 + x = 0.806225775 Solving -5.5 + x = 0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 0.806225775 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 0.806225775 + 5.5 x = 0.806225775 + 5.5 Combine like terms: 0.806225775 + 5.5 = 6.306225775 x = 6.306225775 Simplifying x = 6.306225775Subproblem 2
x + -5.5 = -0.806225775 Simplifying x + -5.5 = -0.806225775 Reorder the terms: -5.5 + x = -0.806225775 Solving -5.5 + x = -0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -0.806225775 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -0.806225775 + 5.5 x = -0.806225775 + 5.5 Combine like terms: -0.806225775 + 5.5 = 4.693774225 x = 4.693774225 Simplifying x = 4.693774225Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.306225775, 4.693774225}
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