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Simplifying (x2 + 2x) + (x2 + 12x) = 80 Reorder the terms: (2x + x2) + (x2 + 12x) = 80 Remove parenthesis around (2x + x2) 2x + x2 + (x2 + 12x) = 80 Reorder the terms: 2x + x2 + (12x + x2) = 80 Remove parenthesis around (12x + x2) 2x + x2 + 12x + x2 = 80 Reorder the terms: 2x + 12x + x2 + x2 = 80 Combine like terms: 2x + 12x = 14x 14x + x2 + x2 = 80 Combine like terms: x2 + x2 = 2x2 14x + 2x2 = 80 Solving 14x + 2x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 14x + 2x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + 7x + x2)' equal to zero and attempt to solve: Simplifying -40 + 7x + x2 = 0 Solving -40 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 7x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 7x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 7x + x2 = 0 + 40 7x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 7x + x2 = 40 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 40 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 40 + 12.25 Combine like terms: 40 + 12.25 = 52.25 12.25 + 7x + x2 = 52.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 3.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 3.5 = 7.228416147 Simplifying x + 3.5 = 7.228416147 Reorder the terms: 3.5 + x = 7.228416147 Solving 3.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 7.228416147 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.228416147 + -3.5 x = 7.228416147 + -3.5 Combine like terms: 7.228416147 + -3.5 = 3.728416147 x = 3.728416147 Simplifying x = 3.728416147Subproblem 2
x + 3.5 = -7.228416147 Simplifying x + 3.5 = -7.228416147 Reorder the terms: 3.5 + x = -7.228416147 Solving 3.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -7.228416147 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.228416147 + -3.5 x = -7.228416147 + -3.5 Combine like terms: -7.228416147 + -3.5 = -10.728416147 x = -10.728416147 Simplifying x = -10.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.728416147, -10.728416147}Solution
x = {3.728416147, -10.728416147}
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