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Simplifying 2x2 + -19x + 40 = 0 Reorder the terms: 40 + -19x + 2x2 = 0 Solving 40 + -19x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 20 + -9.5x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -9.5x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -9.5x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -9.5x + x2 = 0 + -20 -9.5x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -9.5x + x2 = -20 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -20 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -20 + 22.5625 Combine like terms: -20 + 22.5625 = 2.5625 22.5625 + -9.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -4.75) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -4.75 = 1.600781059 Simplifying x + -4.75 = 1.600781059 Reorder the terms: -4.75 + x = 1.600781059 Solving -4.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 1.600781059 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 1.600781059 + 4.75 x = 1.600781059 + 4.75 Combine like terms: 1.600781059 + 4.75 = 6.350781059 x = 6.350781059 Simplifying x = 6.350781059Subproblem 2
x + -4.75 = -1.600781059 Simplifying x + -4.75 = -1.600781059 Reorder the terms: -4.75 + x = -1.600781059 Solving -4.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -1.600781059 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -1.600781059 + 4.75 x = -1.600781059 + 4.75 Combine like terms: -1.600781059 + 4.75 = 3.149218941 x = 3.149218941 Simplifying x = 3.149218941Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.350781059, 3.149218941}
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