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Simplifying 240x2 + 60x + -4 = 0 Reorder the terms: -4 + 60x + 240x2 = 0 Solving -4 + 60x + 240x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 15x + 60x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + 15x + 60x2)' equal to zero and attempt to solve: Simplifying -1 + 15x + 60x2 = 0 Solving -1 + 15x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -0.01666666667 + 0.25x + x2 = 0.0 Move the constant term to the right: Add '0.01666666667' to each side of the equation. -0.01666666667 + 0.25x + 0.01666666667 + x2 = 0.0 + 0.01666666667 Reorder the terms: -0.01666666667 + 0.01666666667 + 0.25x + x2 = 0.0 + 0.01666666667 Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000 0.00000000000 + 0.25x + x2 = 0.0 + 0.01666666667 0.25x + x2 = 0.0 + 0.01666666667 Combine like terms: 0.0 + 0.01666666667 = 0.01666666667 0.25x + x2 = 0.01666666667 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.01666666667 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.01666666667 + 0.015625 Combine like terms: 0.01666666667 + 0.015625 = 0.03229166667 0.015625 + 0.25x + x2 = 0.03229166667 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.03229166667 Calculate the square root of the right side: 0.179698822 Break this problem into two subproblems by setting (x + 0.125) equal to 0.179698822 and -0.179698822.Subproblem 1
x + 0.125 = 0.179698822 Simplifying x + 0.125 = 0.179698822 Reorder the terms: 0.125 + x = 0.179698822 Solving 0.125 + x = 0.179698822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.179698822 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.179698822 + -0.125 x = 0.179698822 + -0.125 Combine like terms: 0.179698822 + -0.125 = 0.054698822 x = 0.054698822 Simplifying x = 0.054698822Subproblem 2
x + 0.125 = -0.179698822 Simplifying x + 0.125 = -0.179698822 Reorder the terms: 0.125 + x = -0.179698822 Solving 0.125 + x = -0.179698822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.179698822 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.179698822 + -0.125 x = -0.179698822 + -0.125 Combine like terms: -0.179698822 + -0.125 = -0.304698822 x = -0.304698822 Simplifying x = -0.304698822Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.054698822, -0.304698822}Solution
x = {0.054698822, -0.304698822}
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