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Simplifying 16x2 + 1000x + 50 = 2000 Reorder the terms: 50 + 1000x + 16x2 = 2000 Solving 50 + 1000x + 16x2 = 2000 Solving for variable 'x'. Reorder the terms: 50 + -2000 + 1000x + 16x2 = 2000 + -2000 Combine like terms: 50 + -2000 = -1950 -1950 + 1000x + 16x2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -1950 + 1000x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-975 + 500x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-975 + 500x + 8x2)' equal to zero and attempt to solve: Simplifying -975 + 500x + 8x2 = 0 Solving -975 + 500x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -121.875 + 62.5x + x2 = 0 Move the constant term to the right: Add '121.875' to each side of the equation. -121.875 + 62.5x + 121.875 + x2 = 0 + 121.875 Reorder the terms: -121.875 + 121.875 + 62.5x + x2 = 0 + 121.875 Combine like terms: -121.875 + 121.875 = 0.000 0.000 + 62.5x + x2 = 0 + 121.875 62.5x + x2 = 0 + 121.875 Combine like terms: 0 + 121.875 = 121.875 62.5x + x2 = 121.875 The x term is 62.5x. Take half its coefficient (31.25). Square it (976.5625) and add it to both sides. Add '976.5625' to each side of the equation. 62.5x + 976.5625 + x2 = 121.875 + 976.5625 Reorder the terms: 976.5625 + 62.5x + x2 = 121.875 + 976.5625 Combine like terms: 121.875 + 976.5625 = 1098.4375 976.5625 + 62.5x + x2 = 1098.4375 Factor a perfect square on the left side: (x + 31.25)(x + 31.25) = 1098.4375 Calculate the square root of the right side: 33.142683959 Break this problem into two subproblems by setting (x + 31.25) equal to 33.142683959 and -33.142683959.Subproblem 1
x + 31.25 = 33.142683959 Simplifying x + 31.25 = 33.142683959 Reorder the terms: 31.25 + x = 33.142683959 Solving 31.25 + x = 33.142683959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.25' to each side of the equation. 31.25 + -31.25 + x = 33.142683959 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + x = 33.142683959 + -31.25 x = 33.142683959 + -31.25 Combine like terms: 33.142683959 + -31.25 = 1.892683959 x = 1.892683959 Simplifying x = 1.892683959Subproblem 2
x + 31.25 = -33.142683959 Simplifying x + 31.25 = -33.142683959 Reorder the terms: 31.25 + x = -33.142683959 Solving 31.25 + x = -33.142683959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.25' to each side of the equation. 31.25 + -31.25 + x = -33.142683959 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + x = -33.142683959 + -31.25 x = -33.142683959 + -31.25 Combine like terms: -33.142683959 + -31.25 = -64.392683959 x = -64.392683959 Simplifying x = -64.392683959Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.892683959, -64.392683959}Solution
x = {1.892683959, -64.392683959}
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