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Simplifying 40x2 + 12x + -39 = 0 Reorder the terms: -39 + 12x + 40x2 = 0 Solving -39 + 12x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.975 + 0.3x + x2 = 0 Move the constant term to the right: Add '0.975' to each side of the equation. -0.975 + 0.3x + 0.975 + x2 = 0 + 0.975 Reorder the terms: -0.975 + 0.975 + 0.3x + x2 = 0 + 0.975 Combine like terms: -0.975 + 0.975 = 0.000 0.000 + 0.3x + x2 = 0 + 0.975 0.3x + x2 = 0 + 0.975 Combine like terms: 0 + 0.975 = 0.975 0.3x + x2 = 0.975 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.975 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.975 + 0.0225 Combine like terms: 0.975 + 0.0225 = 0.9975 0.0225 + 0.3x + x2 = 0.9975 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.9975 Calculate the square root of the right side: 0.998749218 Break this problem into two subproblems by setting (x + 0.15) equal to 0.998749218 and -0.998749218.Subproblem 1
x + 0.15 = 0.998749218 Simplifying x + 0.15 = 0.998749218 Reorder the terms: 0.15 + x = 0.998749218 Solving 0.15 + x = 0.998749218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.998749218 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.998749218 + -0.15 x = 0.998749218 + -0.15 Combine like terms: 0.998749218 + -0.15 = 0.848749218 x = 0.848749218 Simplifying x = 0.848749218Subproblem 2
x + 0.15 = -0.998749218 Simplifying x + 0.15 = -0.998749218 Reorder the terms: 0.15 + x = -0.998749218 Solving 0.15 + x = -0.998749218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.998749218 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.998749218 + -0.15 x = -0.998749218 + -0.15 Combine like terms: -0.998749218 + -0.15 = -1.148749218 x = -1.148749218 Simplifying x = -1.148749218Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.848749218, -1.148749218}
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