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Simplifying x2 + 3x2 = 80 + 8x Combine like terms: x2 + 3x2 = 4x2 4x2 = 80 + 8x Solving 4x2 = 80 + 8x Solving for variable 'x'. Reorder the terms: -80 + -8x + 4x2 = 80 + 8x + -80 + -8x Reorder the terms: -80 + -8x + 4x2 = 80 + -80 + 8x + -8x Combine like terms: 80 + -80 = 0 -80 + -8x + 4x2 = 0 + 8x + -8x -80 + -8x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -80 + -8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + -2x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20 + -2x + x2)' equal to zero and attempt to solve: Simplifying -20 + -2x + x2 = 0 Solving -20 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -2x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -2x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2x + x2 = 0 + 20 -2x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2x + x2 = 20 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 20 + 1 Reorder the terms: 1 + -2x + x2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + -2x + x2 = 21 Factor a perfect square on the left side: (x + -1)(x + -1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -1) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -1 = 4.582575695 Simplifying x + -1 = 4.582575695 Reorder the terms: -1 + x = 4.582575695 Solving -1 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.582575695 + 1 x = 4.582575695 + 1 Combine like terms: 4.582575695 + 1 = 5.582575695 x = 5.582575695 Simplifying x = 5.582575695Subproblem 2
x + -1 = -4.582575695 Simplifying x + -1 = -4.582575695 Reorder the terms: -1 + x = -4.582575695 Solving -1 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.582575695 + 1 x = -4.582575695 + 1 Combine like terms: -4.582575695 + 1 = -3.582575695 x = -3.582575695 Simplifying x = -3.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.582575695, -3.582575695}Solution
x = {5.582575695, -3.582575695}
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