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Simplifying -5x2 + 15x = 11 Reorder the terms: 15x + -5x2 = 11 Solving 15x + -5x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 15x + -5x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 15x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2.2 + -3x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + -3x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + -3x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + -3x + x2 = 0 + -2.2 -3x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 -3x + x2 = -2.2 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2.2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.2 + 2.25 Combine like terms: -2.2 + 2.25 = 0.05 2.25 + -3x + x2 = 0.05 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.05 Calculate the square root of the right side: 0.223606798 Break this problem into two subproblems by setting (x + -1.5) equal to 0.223606798 and -0.223606798.Subproblem 1
x + -1.5 = 0.223606798 Simplifying x + -1.5 = 0.223606798 Reorder the terms: -1.5 + x = 0.223606798 Solving -1.5 + x = 0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.223606798 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.223606798 + 1.5 x = 0.223606798 + 1.5 Combine like terms: 0.223606798 + 1.5 = 1.723606798 x = 1.723606798 Simplifying x = 1.723606798Subproblem 2
x + -1.5 = -0.223606798 Simplifying x + -1.5 = -0.223606798 Reorder the terms: -1.5 + x = -0.223606798 Solving -1.5 + x = -0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.223606798 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.223606798 + 1.5 x = -0.223606798 + 1.5 Combine like terms: -0.223606798 + 1.5 = 1.276393202 x = 1.276393202 Simplifying x = 1.276393202Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.723606798, 1.276393202}
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