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Simplifying 64x2 + 10000x + 10000 = 0 Reorder the terms: 10000 + 10000x + 64x2 = 0 Solving 10000 + 10000x + 64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(625 + 625x + 4x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(625 + 625x + 4x2)' equal to zero and attempt to solve: Simplifying 625 + 625x + 4x2 = 0 Solving 625 + 625x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 156.25 + 156.25x + x2 = 0 Move the constant term to the right: Add '-156.25' to each side of the equation. 156.25 + 156.25x + -156.25 + x2 = 0 + -156.25 Reorder the terms: 156.25 + -156.25 + 156.25x + x2 = 0 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 0.00 + 156.25x + x2 = 0 + -156.25 156.25x + x2 = 0 + -156.25 Combine like terms: 0 + -156.25 = -156.25 156.25x + x2 = -156.25 The x term is 156.25x. Take half its coefficient (78.125). Square it (6103.515625) and add it to both sides. Add '6103.515625' to each side of the equation. 156.25x + 6103.515625 + x2 = -156.25 + 6103.515625 Reorder the terms: 6103.515625 + 156.25x + x2 = -156.25 + 6103.515625 Combine like terms: -156.25 + 6103.515625 = 5947.265625 6103.515625 + 156.25x + x2 = 5947.265625 Factor a perfect square on the left side: (x + 78.125)(x + 78.125) = 5947.265625 Calculate the square root of the right side: 77.118516745 Break this problem into two subproblems by setting (x + 78.125) equal to 77.118516745 and -77.118516745.Subproblem 1
x + 78.125 = 77.118516745 Simplifying x + 78.125 = 77.118516745 Reorder the terms: 78.125 + x = 77.118516745 Solving 78.125 + x = 77.118516745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78.125' to each side of the equation. 78.125 + -78.125 + x = 77.118516745 + -78.125 Combine like terms: 78.125 + -78.125 = 0.000 0.000 + x = 77.118516745 + -78.125 x = 77.118516745 + -78.125 Combine like terms: 77.118516745 + -78.125 = -1.006483255 x = -1.006483255 Simplifying x = -1.006483255Subproblem 2
x + 78.125 = -77.118516745 Simplifying x + 78.125 = -77.118516745 Reorder the terms: 78.125 + x = -77.118516745 Solving 78.125 + x = -77.118516745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78.125' to each side of the equation. 78.125 + -78.125 + x = -77.118516745 + -78.125 Combine like terms: 78.125 + -78.125 = 0.000 0.000 + x = -77.118516745 + -78.125 x = -77.118516745 + -78.125 Combine like terms: -77.118516745 + -78.125 = -155.243516745 x = -155.243516745 Simplifying x = -155.243516745Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.006483255, -155.243516745}Solution
x = {-1.006483255, -155.243516745}
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