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Simplifying 2x(15 + -1x) = 11 (15 * 2x + -1x * 2x) = 11 (30x + -2x2) = 11 Solving 30x + -2x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 30x + -2x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 30x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5.5 + -15x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -15x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -15x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -15x + x2 = 0 + -5.5 -15x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -15x + x2 = -5.5 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -5.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -5.5 + 56.25 Combine like terms: -5.5 + 56.25 = 50.75 56.25 + -15x + x2 = 50.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 50.75 Calculate the square root of the right side: 7.123903424 Break this problem into two subproblems by setting (x + -7.5) equal to 7.123903424 and -7.123903424.Subproblem 1
x + -7.5 = 7.123903424 Simplifying x + -7.5 = 7.123903424 Reorder the terms: -7.5 + x = 7.123903424 Solving -7.5 + x = 7.123903424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.123903424 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.123903424 + 7.5 x = 7.123903424 + 7.5 Combine like terms: 7.123903424 + 7.5 = 14.623903424 x = 14.623903424 Simplifying x = 14.623903424Subproblem 2
x + -7.5 = -7.123903424 Simplifying x + -7.5 = -7.123903424 Reorder the terms: -7.5 + x = -7.123903424 Solving -7.5 + x = -7.123903424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.123903424 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.123903424 + 7.5 x = -7.123903424 + 7.5 Combine like terms: -7.123903424 + 7.5 = 0.376096576 x = 0.376096576 Simplifying x = 0.376096576Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.623903424, 0.376096576}
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