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Simplifying 0.25x2 + -4.5x + 11.25 = 0 Reorder the terms: 11.25 + -4.5x + 0.25x2 = 0 Solving 11.25 + -4.5x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 45 + -18x + x2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + -18x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -18x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -18x + x2 = 0 + -45 -18x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -18x + x2 = -45 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -45 + 81 Reorder the terms: 81 + -18x + x2 = -45 + 81 Combine like terms: -45 + 81 = 36 81 + -18x + x2 = 36 Factor a perfect square on the left side: (x + -9)(x + -9) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -9) equal to 6 and -6.Subproblem 1
x + -9 = 6 Simplifying x + -9 = 6 Reorder the terms: -9 + x = 6 Solving -9 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 6 + 9 Combine like terms: -9 + 9 = 0 0 + x = 6 + 9 x = 6 + 9 Combine like terms: 6 + 9 = 15 x = 15 Simplifying x = 15Subproblem 2
x + -9 = -6 Simplifying x + -9 = -6 Reorder the terms: -9 + x = -6 Solving -9 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -6 + 9 Combine like terms: -9 + 9 = 0 0 + x = -6 + 9 x = -6 + 9 Combine like terms: -6 + 9 = 3 x = 3 Simplifying x = 3Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, 3}
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