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Simplifying 4x2 + 4x + -80 = 1012 Reorder the terms: -80 + 4x + 4x2 = 1012 Solving -80 + 4x + 4x2 = 1012 Solving for variable 'x'. Reorder the terms: -80 + -1012 + 4x + 4x2 = 1012 + -1012 Combine like terms: -80 + -1012 = -1092 -1092 + 4x + 4x2 = 1012 + -1012 Combine like terms: 1012 + -1012 = 0 -1092 + 4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-273 + x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-273 + x + x2)' equal to zero and attempt to solve: Simplifying -273 + x + x2 = 0 Solving -273 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '273' to each side of the equation. -273 + x + 273 + x2 = 0 + 273 Reorder the terms: -273 + 273 + x + x2 = 0 + 273 Combine like terms: -273 + 273 = 0 0 + x + x2 = 0 + 273 x + x2 = 0 + 273 Combine like terms: 0 + 273 = 273 x + x2 = 273 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 273 + 0.25 Reorder the terms: 0.25 + x + x2 = 273 + 0.25 Combine like terms: 273 + 0.25 = 273.25 0.25 + x + x2 = 273.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 273.25 Calculate the square root of the right side: 16.530275255 Break this problem into two subproblems by setting (x + 0.5) equal to 16.530275255 and -16.530275255.Subproblem 1
x + 0.5 = 16.530275255 Simplifying x + 0.5 = 16.530275255 Reorder the terms: 0.5 + x = 16.530275255 Solving 0.5 + x = 16.530275255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 16.530275255 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.530275255 + -0.5 x = 16.530275255 + -0.5 Combine like terms: 16.530275255 + -0.5 = 16.030275255 x = 16.030275255 Simplifying x = 16.030275255Subproblem 2
x + 0.5 = -16.530275255 Simplifying x + 0.5 = -16.530275255 Reorder the terms: 0.5 + x = -16.530275255 Solving 0.5 + x = -16.530275255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -16.530275255 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.530275255 + -0.5 x = -16.530275255 + -0.5 Combine like terms: -16.530275255 + -0.5 = -17.030275255 x = -17.030275255 Simplifying x = -17.030275255Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.030275255, -17.030275255}Solution
x = {16.030275255, -17.030275255}
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