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Simplifying (16 + -2x)(11 + -2x) = 86 Multiply (16 + -2x) * (11 + -2x) (16(11 + -2x) + -2x * (11 + -2x)) = 86 ((11 * 16 + -2x * 16) + -2x * (11 + -2x)) = 86 ((176 + -32x) + -2x * (11 + -2x)) = 86 (176 + -32x + (11 * -2x + -2x * -2x)) = 86 (176 + -32x + (-22x + 4x2)) = 86 Combine like terms: -32x + -22x = -54x (176 + -54x + 4x2) = 86 Solving 176 + -54x + 4x2 = 86 Solving for variable 'x'. Reorder the terms: 176 + -86 + -54x + 4x2 = 86 + -86 Combine like terms: 176 + -86 = 90 90 + -54x + 4x2 = 86 + -86 Combine like terms: 86 + -86 = 0 90 + -54x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -27x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -27x + 2x2)' equal to zero and attempt to solve: Simplifying 45 + -27x + 2x2 = 0 Solving 45 + -27x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + -13.5x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -13.5x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -13.5x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -13.5x + x2 = 0 + -22.5 -13.5x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -13.5x + x2 = -22.5 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -22.5 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -22.5 + 45.5625 Combine like terms: -22.5 + 45.5625 = 23.0625 45.5625 + -13.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + -6.75) equal to 4.802343178 and -4.802343178.Subproblem 1
x + -6.75 = 4.802343178 Simplifying x + -6.75 = 4.802343178 Reorder the terms: -6.75 + x = 4.802343178 Solving -6.75 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 4.802343178 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 4.802343178 + 6.75 x = 4.802343178 + 6.75 Combine like terms: 4.802343178 + 6.75 = 11.552343178 x = 11.552343178 Simplifying x = 11.552343178Subproblem 2
x + -6.75 = -4.802343178 Simplifying x + -6.75 = -4.802343178 Reorder the terms: -6.75 + x = -4.802343178 Solving -6.75 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -4.802343178 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -4.802343178 + 6.75 x = -4.802343178 + 6.75 Combine like terms: -4.802343178 + 6.75 = 1.947656822 x = 1.947656822 Simplifying x = 1.947656822Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.552343178, 1.947656822}Solution
x = {11.552343178, 1.947656822}
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