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Simplifying 2x2 + -100x + 8 = 0 Reorder the terms: 8 + -100x + 2x2 = 0 Solving 8 + -100x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -50x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -50x + x2)' equal to zero and attempt to solve: Simplifying 4 + -50x + x2 = 0 Solving 4 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -50x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -50x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -50x + x2 = 0 + -4 -50x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -50x + x2 = -4 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -4 + 625 Reorder the terms: 625 + -50x + x2 = -4 + 625 Combine like terms: -4 + 625 = 621 625 + -50x + x2 = 621 Factor a perfect square on the left side: (x + -25)(x + -25) = 621 Calculate the square root of the right side: 24.919871589 Break this problem into two subproblems by setting (x + -25) equal to 24.919871589 and -24.919871589.Subproblem 1
x + -25 = 24.919871589 Simplifying x + -25 = 24.919871589 Reorder the terms: -25 + x = 24.919871589 Solving -25 + x = 24.919871589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 24.919871589 + 25 Combine like terms: -25 + 25 = 0 0 + x = 24.919871589 + 25 x = 24.919871589 + 25 Combine like terms: 24.919871589 + 25 = 49.919871589 x = 49.919871589 Simplifying x = 49.919871589Subproblem 2
x + -25 = -24.919871589 Simplifying x + -25 = -24.919871589 Reorder the terms: -25 + x = -24.919871589 Solving -25 + x = -24.919871589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -24.919871589 + 25 Combine like terms: -25 + 25 = 0 0 + x = -24.919871589 + 25 x = -24.919871589 + 25 Combine like terms: -24.919871589 + 25 = 0.080128411 x = 0.080128411 Simplifying x = 0.080128411Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.919871589, 0.080128411}Solution
x = {49.919871589, 0.080128411}
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