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Simplifying 900 + -300x + 12x2 = 0 Solving 900 + -300x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(75 + -25x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(75 + -25x + x2)' equal to zero and attempt to solve: Simplifying 75 + -25x + x2 = 0 Solving 75 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + -25x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -25x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -25x + x2 = 0 + -75 -25x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -25x + x2 = -75 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -75 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -75 + 156.25 Combine like terms: -75 + 156.25 = 81.25 156.25 + -25x + x2 = 81.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + -12.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + -12.5 = 9.013878189 Simplifying x + -12.5 = 9.013878189 Reorder the terms: -12.5 + x = 9.013878189 Solving -12.5 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 9.013878189 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 9.013878189 + 12.5 x = 9.013878189 + 12.5 Combine like terms: 9.013878189 + 12.5 = 21.513878189 x = 21.513878189 Simplifying x = 21.513878189Subproblem 2
x + -12.5 = -9.013878189 Simplifying x + -12.5 = -9.013878189 Reorder the terms: -12.5 + x = -9.013878189 Solving -12.5 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -9.013878189 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -9.013878189 + 12.5 x = -9.013878189 + 12.5 Combine like terms: -9.013878189 + 12.5 = 3.486121811 x = 3.486121811 Simplifying x = 3.486121811Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.513878189, 3.486121811}Solution
x = {21.513878189, 3.486121811}
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