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Simplifying 80 = -32x2 + 22500x Reorder the terms: 80 = 22500x + -32x2 Solving 80 = 22500x + -32x2 Solving for variable 'x'. Reorder the terms: 80 + -22500x + 32x2 = 22500x + -22500x + -32x2 + 32x2 Combine like terms: 22500x + -22500x = 0 80 + -22500x + 32x2 = 0 + -32x2 + 32x2 80 + -22500x + 32x2 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 80 + -22500x + 32x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(20 + -5625x + 8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(20 + -5625x + 8x2)' equal to zero and attempt to solve: Simplifying 20 + -5625x + 8x2 = 0 Solving 20 + -5625x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.5 + -703.125x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -703.125x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -703.125x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -703.125x + x2 = 0 + -2.5 -703.125x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -703.125x + x2 = -2.5 The x term is -703.125x. Take half its coefficient (-351.5625). Square it (123596.1914) and add it to both sides. Add '123596.1914' to each side of the equation. -703.125x + 123596.1914 + x2 = -2.5 + 123596.1914 Reorder the terms: 123596.1914 + -703.125x + x2 = -2.5 + 123596.1914 Combine like terms: -2.5 + 123596.1914 = 123593.6914 123596.1914 + -703.125x + x2 = 123593.6914 Factor a perfect square on the left side: (x + -351.5625)(x + -351.5625) = 123593.6914 Calculate the square root of the right side: 351.558944418 Break this problem into two subproblems by setting (x + -351.5625) equal to 351.558944418 and -351.558944418.Subproblem 1
x + -351.5625 = 351.558944418 Simplifying x + -351.5625 = 351.558944418 Reorder the terms: -351.5625 + x = 351.558944418 Solving -351.5625 + x = 351.558944418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '351.5625' to each side of the equation. -351.5625 + 351.5625 + x = 351.558944418 + 351.5625 Combine like terms: -351.5625 + 351.5625 = 0.0000 0.0000 + x = 351.558944418 + 351.5625 x = 351.558944418 + 351.5625 Combine like terms: 351.558944418 + 351.5625 = 703.121444418 x = 703.121444418 Simplifying x = 703.121444418Subproblem 2
x + -351.5625 = -351.558944418 Simplifying x + -351.5625 = -351.558944418 Reorder the terms: -351.5625 + x = -351.558944418 Solving -351.5625 + x = -351.558944418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '351.5625' to each side of the equation. -351.5625 + 351.5625 + x = -351.558944418 + 351.5625 Combine like terms: -351.5625 + 351.5625 = 0.0000 0.0000 + x = -351.558944418 + 351.5625 x = -351.558944418 + 351.5625 Combine like terms: -351.558944418 + 351.5625 = 0.003555582 x = 0.003555582 Simplifying x = 0.003555582Solution
The solution to the problem is based on the solutions from the subproblems. x = {703.121444418, 0.003555582}Solution
x = {703.121444418, 0.003555582}
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