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Simplifying -3x(x + 11) = -15 Reorder the terms: -3x(11 + x) = -15 (11 * -3x + x * -3x) = -15 (-33x + -3x2) = -15 Solving -33x + -3x2 = -15 Solving for variable 'x'. Reorder the terms: 15 + -33x + -3x2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -33x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -11x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -11x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -11x + -1x2 = 0 Solving 5 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 11x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 11x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 11x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 11x + x2 = 0 + 5 11x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 11x + x2 = 5 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 5 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 5 + 30.25 Combine like terms: 5 + 30.25 = 35.25 30.25 + 11x + x2 = 35.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 5.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 5.5 = 5.937171044 Simplifying x + 5.5 = 5.937171044 Reorder the terms: 5.5 + x = 5.937171044 Solving 5.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 5.937171044 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.937171044 + -5.5 x = 5.937171044 + -5.5 Combine like terms: 5.937171044 + -5.5 = 0.437171044 x = 0.437171044 Simplifying x = 0.437171044Subproblem 2
x + 5.5 = -5.937171044 Simplifying x + 5.5 = -5.937171044 Reorder the terms: 5.5 + x = -5.937171044 Solving 5.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -5.937171044 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.937171044 + -5.5 x = -5.937171044 + -5.5 Combine like terms: -5.937171044 + -5.5 = -11.437171044 x = -11.437171044 Simplifying x = -11.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.437171044, -11.437171044}Solution
x = {0.437171044, -11.437171044}
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