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Simplifying x2 + -6x + 9 + 4x2 + 36x + 81 = 100 Reorder the terms: 9 + 81 + -6x + 36x + x2 + 4x2 = 100 Combine like terms: 9 + 81 = 90 90 + -6x + 36x + x2 + 4x2 = 100 Combine like terms: -6x + 36x = 30x 90 + 30x + x2 + 4x2 = 100 Combine like terms: x2 + 4x2 = 5x2 90 + 30x + 5x2 = 100 Solving 90 + 30x + 5x2 = 100 Solving for variable 'x'. Reorder the terms: 90 + -100 + 30x + 5x2 = 100 + -100 Combine like terms: 90 + -100 = -10 -10 + 30x + 5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -10 + 30x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 6x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + 6x + x2)' equal to zero and attempt to solve: Simplifying -2 + 6x + x2 = 0 Solving -2 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6x + x2 = 0 + 2 6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6x + x2 = 2 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2 + 9 Reorder the terms: 9 + 6x + x2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6x + x2 = 11 Factor a perfect square on the left side: (x + 3)(x + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 3 = 3.31662479 Simplifying x + 3 = 3.31662479 Reorder the terms: 3 + x = 3.31662479 Solving 3 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.31662479 + -3 x = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 x = 0.31662479 Simplifying x = 0.31662479Subproblem 2
x + 3 = -3.31662479 Simplifying x + 3 = -3.31662479 Reorder the terms: 3 + x = -3.31662479 Solving 3 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.31662479 + -3 x = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 x = -6.31662479 Simplifying x = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31662479, -6.31662479}Solution
x = {0.31662479, -6.31662479}
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