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Simplifying 4x2 + -92x + -100 = 0 Reorder the terms: -100 + -92x + 4x2 = 0 Solving -100 + -92x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -23x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -23x + x2)' equal to zero and attempt to solve: Simplifying -25 + -23x + x2 = 0 Solving -25 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -23x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -23x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -23x + x2 = 0 + 25 -23x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -23x + x2 = 25 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = 25 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 25 + 132.25 Combine like terms: 25 + 132.25 = 157.25 132.25 + -23x + x2 = 157.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 157.25 Calculate the square root of the right side: 12.539936204 Break this problem into two subproblems by setting (x + -11.5) equal to 12.539936204 and -12.539936204.Subproblem 1
x + -11.5 = 12.539936204 Simplifying x + -11.5 = 12.539936204 Reorder the terms: -11.5 + x = 12.539936204 Solving -11.5 + x = 12.539936204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 12.539936204 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 12.539936204 + 11.5 x = 12.539936204 + 11.5 Combine like terms: 12.539936204 + 11.5 = 24.039936204 x = 24.039936204 Simplifying x = 24.039936204Subproblem 2
x + -11.5 = -12.539936204 Simplifying x + -11.5 = -12.539936204 Reorder the terms: -11.5 + x = -12.539936204 Solving -11.5 + x = -12.539936204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -12.539936204 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -12.539936204 + 11.5 x = -12.539936204 + 11.5 Combine like terms: -12.539936204 + 11.5 = -1.039936204 x = -1.039936204 Simplifying x = -1.039936204Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.039936204, -1.039936204}Solution
x = {24.039936204, -1.039936204}
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