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Simplifying 4x2 + -36x + 80 = 208 Reorder the terms: 80 + -36x + 4x2 = 208 Solving 80 + -36x + 4x2 = 208 Solving for variable 'x'. Reorder the terms: 80 + -208 + -36x + 4x2 = 208 + -208 Combine like terms: 80 + -208 = -128 -128 + -36x + 4x2 = 208 + -208 Combine like terms: 208 + -208 = 0 -128 + -36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-32 + -9x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-32 + -9x + x2)' equal to zero and attempt to solve: Simplifying -32 + -9x + x2 = 0 Solving -32 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -9x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -9x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -9x + x2 = 0 + 32 -9x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -9x + x2 = 32 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 32 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 32 + 20.25 Combine like terms: 32 + 20.25 = 52.25 20.25 + -9x + x2 = 52.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + -4.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + -4.5 = 7.228416147 Simplifying x + -4.5 = 7.228416147 Reorder the terms: -4.5 + x = 7.228416147 Solving -4.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 7.228416147 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.228416147 + 4.5 x = 7.228416147 + 4.5 Combine like terms: 7.228416147 + 4.5 = 11.728416147 x = 11.728416147 Simplifying x = 11.728416147Subproblem 2
x + -4.5 = -7.228416147 Simplifying x + -4.5 = -7.228416147 Reorder the terms: -4.5 + x = -7.228416147 Solving -4.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -7.228416147 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.228416147 + 4.5 x = -7.228416147 + 4.5 Combine like terms: -7.228416147 + 4.5 = -2.728416147 x = -2.728416147 Simplifying x = -2.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.728416147, -2.728416147}Solution
x = {11.728416147, -2.728416147}
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