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Simplifying -4x2 + -19x + 40 = 0 Reorder the terms: 40 + -19x + -4x2 = 0 Solving 40 + -19x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -10 + 4.75x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 4.75x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 4.75x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4.75x + x2 = 0 + 10 4.75x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 4.75x + x2 = 10 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 10 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 10 + 5.640625 Combine like terms: 10 + 5.640625 = 15.640625 5.640625 + 4.75x + x2 = 15.640625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 15.640625 Calculate the square root of the right side: 3.954823005 Break this problem into two subproblems by setting (x + 2.375) equal to 3.954823005 and -3.954823005.Subproblem 1
x + 2.375 = 3.954823005 Simplifying x + 2.375 = 3.954823005 Reorder the terms: 2.375 + x = 3.954823005 Solving 2.375 + x = 3.954823005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 3.954823005 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 3.954823005 + -2.375 x = 3.954823005 + -2.375 Combine like terms: 3.954823005 + -2.375 = 1.579823005 x = 1.579823005 Simplifying x = 1.579823005Subproblem 2
x + 2.375 = -3.954823005 Simplifying x + 2.375 = -3.954823005 Reorder the terms: 2.375 + x = -3.954823005 Solving 2.375 + x = -3.954823005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -3.954823005 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -3.954823005 + -2.375 x = -3.954823005 + -2.375 Combine like terms: -3.954823005 + -2.375 = -6.329823005 x = -6.329823005 Simplifying x = -6.329823005Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.579823005, -6.329823005}
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