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Simplifying 2x2 = 22 + 10x Solving 2x2 = 22 + 10x Solving for variable 'x'. Reorder the terms: -22 + -10x + 2x2 = 22 + 10x + -22 + -10x Reorder the terms: -22 + -10x + 2x2 = 22 + -22 + 10x + -10x Combine like terms: 22 + -22 = 0 -22 + -10x + 2x2 = 0 + 10x + -10x -22 + -10x + 2x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -22 + -10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + -5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -5x + x2)' equal to zero and attempt to solve: Simplifying -11 + -5x + x2 = 0 Solving -11 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -5x + x2 = 0 + 11 -5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -5x + x2 = 11 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 11 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 11 + 6.25 Combine like terms: 11 + 6.25 = 17.25 6.25 + -5x + x2 = 17.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -2.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -2.5 = 4.153311931 Simplifying x + -2.5 = 4.153311931 Reorder the terms: -2.5 + x = 4.153311931 Solving -2.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.153311931 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.153311931 + 2.5 x = 4.153311931 + 2.5 Combine like terms: 4.153311931 + 2.5 = 6.653311931 x = 6.653311931 Simplifying x = 6.653311931Subproblem 2
x + -2.5 = -4.153311931 Simplifying x + -2.5 = -4.153311931 Reorder the terms: -2.5 + x = -4.153311931 Solving -2.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.153311931 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.153311931 + 2.5 x = -4.153311931 + 2.5 Combine like terms: -4.153311931 + 2.5 = -1.653311931 x = -1.653311931 Simplifying x = -1.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.653311931, -1.653311931}Solution
x = {6.653311931, -1.653311931}
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