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Simplifying 30.25 = x2 + -6x + 39 Reorder the terms: 30.25 = 39 + -6x + x2 Solving 30.25 = 39 + -6x + x2 Solving for variable 'x'. Combine like terms: 30.25 + -39 = -8.75 -8.75 + 6x + -1x2 = 39 + -6x + x2 + -39 + 6x + -1x2 Reorder the terms: -8.75 + 6x + -1x2 = 39 + -39 + -6x + 6x + x2 + -1x2 Combine like terms: 39 + -39 = 0 -8.75 + 6x + -1x2 = 0 + -6x + 6x + x2 + -1x2 -8.75 + 6x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -8.75 + 6x + -1x2 = 0 + x2 + -1x2 -8.75 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8.75 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8.75 + -6x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + -6x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + -6x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + -6x + x2 = 0 + -8.75 -6x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 -6x + x2 = -8.75 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -8.75 + 9 Reorder the terms: 9 + -6x + x2 = -8.75 + 9 Combine like terms: -8.75 + 9 = 0.25 9 + -6x + x2 = 0.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + -3) equal to 0.5 and -0.5.Subproblem 1
x + -3 = 0.5 Simplifying x + -3 = 0.5 Reorder the terms: -3 + x = 0.5 Solving -3 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0.5 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0.5 + 3 x = 0.5 + 3 Combine like terms: 0.5 + 3 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + -3 = -0.5 Simplifying x + -3 = -0.5 Reorder the terms: -3 + x = -0.5 Solving -3 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -0.5 + 3 Combine like terms: -3 + 3 = 0 0 + x = -0.5 + 3 x = -0.5 + 3 Combine like terms: -0.5 + 3 = 2.5 x = 2.5 Simplifying x = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, 2.5}
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