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Simplifying 20x2 + 3x = 40 Reorder the terms: 3x + 20x2 = 40 Solving 3x + 20x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + 3x + 20x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 3x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -2 + 0.15x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.15x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.15x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.15x + x2 = 0 + 2 0.15x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.15x + x2 = 2 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = 2 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 2 + 0.005625 Combine like terms: 2 + 0.005625 = 2.005625 0.005625 + 0.15x + x2 = 2.005625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 2.005625 Calculate the square root of the right side: 1.416200904 Break this problem into two subproblems by setting (x + 0.075) equal to 1.416200904 and -1.416200904.Subproblem 1
x + 0.075 = 1.416200904 Simplifying x + 0.075 = 1.416200904 Reorder the terms: 0.075 + x = 1.416200904 Solving 0.075 + x = 1.416200904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 1.416200904 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 1.416200904 + -0.075 x = 1.416200904 + -0.075 Combine like terms: 1.416200904 + -0.075 = 1.341200904 x = 1.341200904 Simplifying x = 1.341200904Subproblem 2
x + 0.075 = -1.416200904 Simplifying x + 0.075 = -1.416200904 Reorder the terms: 0.075 + x = -1.416200904 Solving 0.075 + x = -1.416200904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -1.416200904 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -1.416200904 + -0.075 x = -1.416200904 + -0.075 Combine like terms: -1.416200904 + -0.075 = -1.491200904 x = -1.491200904 Simplifying x = -1.491200904Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.341200904, -1.491200904}
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