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Simplifying -300 = 4x2 + 100x Reorder the terms: -300 = 100x + 4x2 Solving -300 = 100x + 4x2 Solving for variable 'x'. Reorder the terms: -300 + -100x + -4x2 = 100x + -100x + 4x2 + -4x2 Combine like terms: 100x + -100x = 0 -300 + -100x + -4x2 = 0 + 4x2 + -4x2 -300 + -100x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -300 + -100x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(75 + 25x + x2) = 0 Ignore the factor -4.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 = -3.486121811 x = -3.486121811 Simplifying x = -3.486121811Subproblem 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 = -21.513878189 x = -21.513878189 Simplifying x = -21.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.486121811, -21.513878189}Solution
x = {-3.486121811, -21.513878189}
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