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Simplifying 0.64x2 + -0.2x = 3413 Reorder the terms: -0.2x + 0.64x2 = 3413 Solving -0.2x + 0.64x2 = 3413 Solving for variable 'x'. Reorder the terms: -3413 + -0.2x + 0.64x2 = 3413 + -3413 Combine like terms: 3413 + -3413 = 0 -3413 + -0.2x + 0.64x2 = 0 Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. -5332.8125 + -0.3125x + x2 = 0 Move the constant term to the right: Add '5332.8125' to each side of the equation. -5332.8125 + -0.3125x + 5332.8125 + x2 = 0 + 5332.8125 Reorder the terms: -5332.8125 + 5332.8125 + -0.3125x + x2 = 0 + 5332.8125 Combine like terms: -5332.8125 + 5332.8125 = 0.0000 0.0000 + -0.3125x + x2 = 0 + 5332.8125 -0.3125x + x2 = 0 + 5332.8125 Combine like terms: 0 + 5332.8125 = 5332.8125 -0.3125x + x2 = 5332.8125 The x term is -0.3125x. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125x + 0.0244140625 + x2 = 5332.8125 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125x + x2 = 5332.8125 + 0.0244140625 Combine like terms: 5332.8125 + 0.0244140625 = 5332.8369140625 0.0244140625 + -0.3125x + x2 = 5332.8369140625 Factor a perfect square on the left side: (x + -0.15625)(x + -0.15625) = 5332.8369140625 Calculate the square root of the right side: 73.026275505 Break this problem into two subproblems by setting (x + -0.15625) equal to 73.026275505 and -73.026275505.Subproblem 1
x + -0.15625 = 73.026275505 Simplifying x + -0.15625 = 73.026275505 Reorder the terms: -0.15625 + x = 73.026275505 Solving -0.15625 + x = 73.026275505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = 73.026275505 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = 73.026275505 + 0.15625 x = 73.026275505 + 0.15625 Combine like terms: 73.026275505 + 0.15625 = 73.182525505 x = 73.182525505 Simplifying x = 73.182525505Subproblem 2
x + -0.15625 = -73.026275505 Simplifying x + -0.15625 = -73.026275505 Reorder the terms: -0.15625 + x = -73.026275505 Solving -0.15625 + x = -73.026275505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = -73.026275505 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = -73.026275505 + 0.15625 x = -73.026275505 + 0.15625 Combine like terms: -73.026275505 + 0.15625 = -72.870025505 x = -72.870025505 Simplifying x = -72.870025505Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.182525505, -72.870025505}
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