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Simplifying 0 = 39x2 + -64x + 2 Reorder the terms: 0 = 2 + -64x + 39x2 Solving 0 = 2 + -64x + 39x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + 64x + -39x2 = 2 + -64x + 39x2 + -2 + 64x + -39x2 Reorder the terms: -2 + 64x + -39x2 = 2 + -2 + -64x + 64x + 39x2 + -39x2 Combine like terms: 2 + -2 = 0 -2 + 64x + -39x2 = 0 + -64x + 64x + 39x2 + -39x2 -2 + 64x + -39x2 = -64x + 64x + 39x2 + -39x2 Combine like terms: -64x + 64x = 0 -2 + 64x + -39x2 = 0 + 39x2 + -39x2 -2 + 64x + -39x2 = 39x2 + -39x2 Combine like terms: 39x2 + -39x2 = 0 -2 + 64x + -39x2 = 0 Begin completing the square. Divide all terms by -39 the coefficient of the squared term: Divide each side by '-39'. 0.05128205128 + -1.641025641x + x2 = 0 Move the constant term to the right: Add '-0.05128205128' to each side of the equation. 0.05128205128 + -1.641025641x + -0.05128205128 + x2 = 0 + -0.05128205128 Reorder the terms: 0.05128205128 + -0.05128205128 + -1.641025641x + x2 = 0 + -0.05128205128 Combine like terms: 0.05128205128 + -0.05128205128 = 0.00000000000 0.00000000000 + -1.641025641x + x2 = 0 + -0.05128205128 -1.641025641x + x2 = 0 + -0.05128205128 Combine like terms: 0 + -0.05128205128 = -0.05128205128 -1.641025641x + x2 = -0.05128205128 The x term is -1.641025641x. Take half its coefficient (-0.8205128205). Square it (0.6732412886) and add it to both sides. Add '0.6732412886' to each side of the equation. -1.641025641x + 0.6732412886 + x2 = -0.05128205128 + 0.6732412886 Reorder the terms: 0.6732412886 + -1.641025641x + x2 = -0.05128205128 + 0.6732412886 Combine like terms: -0.05128205128 + 0.6732412886 = 0.62195923732 0.6732412886 + -1.641025641x + x2 = 0.62195923732 Factor a perfect square on the left side: (x + -0.8205128205)(x + -0.8205128205) = 0.62195923732 Calculate the square root of the right side: 0.788643923 Break this problem into two subproblems by setting (x + -0.8205128205) equal to 0.788643923 and -0.788643923.Subproblem 1
x + -0.8205128205 = 0.788643923 Simplifying x + -0.8205128205 = 0.788643923 Reorder the terms: -0.8205128205 + x = 0.788643923 Solving -0.8205128205 + x = 0.788643923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8205128205' to each side of the equation. -0.8205128205 + 0.8205128205 + x = 0.788643923 + 0.8205128205 Combine like terms: -0.8205128205 + 0.8205128205 = 0.0000000000 0.0000000000 + x = 0.788643923 + 0.8205128205 x = 0.788643923 + 0.8205128205 Combine like terms: 0.788643923 + 0.8205128205 = 1.6091567435 x = 1.6091567435 Simplifying x = 1.6091567435Subproblem 2
x + -0.8205128205 = -0.788643923 Simplifying x + -0.8205128205 = -0.788643923 Reorder the terms: -0.8205128205 + x = -0.788643923 Solving -0.8205128205 + x = -0.788643923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8205128205' to each side of the equation. -0.8205128205 + 0.8205128205 + x = -0.788643923 + 0.8205128205 Combine like terms: -0.8205128205 + 0.8205128205 = 0.0000000000 0.0000000000 + x = -0.788643923 + 0.8205128205 x = -0.788643923 + 0.8205128205 Combine like terms: -0.788643923 + 0.8205128205 = 0.0318688975 x = 0.0318688975 Simplifying x = 0.0318688975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6091567435, 0.0318688975}
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