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Simplifying -32x * x + 120 * 120x + -80 * 120 * 120 = 0 Multiply x * x -32x2 + 120 * 120x + -80 * 120 * 120 = 0 Multiply 120 * 120 -32x2 + 14400x + -80 * 120 * 120 = 0 Multiply -80 * 120 -32x2 + 14400x + -9600 * 120 = 0 Multiply -9600 * 120 -32x2 + 14400x + -1152000 = 0 Reorder the terms: -1152000 + 14400x + -32x2 = 0 Solving -1152000 + 14400x + -32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '32'. 32(-36000 + 450x + -1x2) = 0 Ignore the factor 32.Subproblem 1
Set the factor '(-36000 + 450x + -1x2)' equal to zero and attempt to solve: Simplifying -36000 + 450x + -1x2 = 0 Solving -36000 + 450x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36000 + -450x + x2 = 0 Move the constant term to the right: Add '-36000' to each side of the equation. 36000 + -450x + -36000 + x2 = 0 + -36000 Reorder the terms: 36000 + -36000 + -450x + x2 = 0 + -36000 Combine like terms: 36000 + -36000 = 0 0 + -450x + x2 = 0 + -36000 -450x + x2 = 0 + -36000 Combine like terms: 0 + -36000 = -36000 -450x + x2 = -36000 The x term is -450x. Take half its coefficient (-225). Square it (50625) and add it to both sides. Add '50625' to each side of the equation. -450x + 50625 + x2 = -36000 + 50625 Reorder the terms: 50625 + -450x + x2 = -36000 + 50625 Combine like terms: -36000 + 50625 = 14625 50625 + -450x + x2 = 14625 Factor a perfect square on the left side: (x + -225)(x + -225) = 14625 Calculate the square root of the right side: 120.933866224 Break this problem into two subproblems by setting (x + -225) equal to 120.933866224 and -120.933866224.Subproblem 1
x + -225 = 120.933866224 Simplifying x + -225 = 120.933866224 Reorder the terms: -225 + x = 120.933866224 Solving -225 + x = 120.933866224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '225' to each side of the equation. -225 + 225 + x = 120.933866224 + 225 Combine like terms: -225 + 225 = 0 0 + x = 120.933866224 + 225 x = 120.933866224 + 225 Combine like terms: 120.933866224 + 225 = 345.933866224 x = 345.933866224 Simplifying x = 345.933866224Subproblem 2
x + -225 = -120.933866224 Simplifying x + -225 = -120.933866224 Reorder the terms: -225 + x = -120.933866224 Solving -225 + x = -120.933866224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '225' to each side of the equation. -225 + 225 + x = -120.933866224 + 225 Combine like terms: -225 + 225 = 0 0 + x = -120.933866224 + 225 x = -120.933866224 + 225 Combine like terms: -120.933866224 + 225 = 104.066133776 x = 104.066133776 Simplifying x = 104.066133776Solution
The solution to the problem is based on the solutions from the subproblems. x = {345.933866224, 104.066133776}Solution
x = {345.933866224, 104.066133776}
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