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Simplifying x(7.5 + -1x) = 11 (7.5 * x + -1x * x) = 11 (7.5x + -1x2) = 11 Solving 7.5x + -1x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 7.5x + -1x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 7.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -7.5x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -7.5x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -7.5x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -7.5x + x2 = 0 + -11 -7.5x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -7.5x + x2 = -11 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -11 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -11 + 14.0625 Combine like terms: -11 + 14.0625 = 3.0625 14.0625 + -7.5x + x2 = 3.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 3.0625 Calculate the square root of the right side: 1.75 Break this problem into two subproblems by setting (x + -3.75) equal to 1.75 and -1.75.Subproblem 1
x + -3.75 = 1.75 Simplifying x + -3.75 = 1.75 Reorder the terms: -3.75 + x = 1.75 Solving -3.75 + x = 1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 1.75 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 1.75 + 3.75 x = 1.75 + 3.75 Combine like terms: 1.75 + 3.75 = 5.5 x = 5.5 Simplifying x = 5.5Subproblem 2
x + -3.75 = -1.75 Simplifying x + -3.75 = -1.75 Reorder the terms: -3.75 + x = -1.75 Solving -3.75 + x = -1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -1.75 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -1.75 + 3.75 x = -1.75 + 3.75 Combine like terms: -1.75 + 3.75 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5, 2}
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