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Simplifying 3x2 + 8x2 + -15x + -40 = 0 Reorder the terms: -40 + -15x + 3x2 + 8x2 = 0 Combine like terms: 3x2 + 8x2 = 11x2 -40 + -15x + 11x2 = 0 Solving -40 + -15x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -3.636363636 + -1.363636364x + x2 = 0 Move the constant term to the right: Add '3.636363636' to each side of the equation. -3.636363636 + -1.363636364x + 3.636363636 + x2 = 0 + 3.636363636 Reorder the terms: -3.636363636 + 3.636363636 + -1.363636364x + x2 = 0 + 3.636363636 Combine like terms: -3.636363636 + 3.636363636 = 0.000000000 0.000000000 + -1.363636364x + x2 = 0 + 3.636363636 -1.363636364x + x2 = 0 + 3.636363636 Combine like terms: 0 + 3.636363636 = 3.636363636 -1.363636364x + x2 = 3.636363636 The x term is -1.363636364x. Take half its coefficient (-0.681818182). Square it (0.4648760333) and add it to both sides. Add '0.4648760333' to each side of the equation. -1.363636364x + 0.4648760333 + x2 = 3.636363636 + 0.4648760333 Reorder the terms: 0.4648760333 + -1.363636364x + x2 = 3.636363636 + 0.4648760333 Combine like terms: 3.636363636 + 0.4648760333 = 4.1012396693 0.4648760333 + -1.363636364x + x2 = 4.1012396693 Factor a perfect square on the left side: (x + -0.681818182)(x + -0.681818182) = 4.1012396693 Calculate the square root of the right side: 2.025151765 Break this problem into two subproblems by setting (x + -0.681818182) equal to 2.025151765 and -2.025151765.Subproblem 1
x + -0.681818182 = 2.025151765 Simplifying x + -0.681818182 = 2.025151765 Reorder the terms: -0.681818182 + x = 2.025151765 Solving -0.681818182 + x = 2.025151765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.681818182' to each side of the equation. -0.681818182 + 0.681818182 + x = 2.025151765 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + x = 2.025151765 + 0.681818182 x = 2.025151765 + 0.681818182 Combine like terms: 2.025151765 + 0.681818182 = 2.706969947 x = 2.706969947 Simplifying x = 2.706969947Subproblem 2
x + -0.681818182 = -2.025151765 Simplifying x + -0.681818182 = -2.025151765 Reorder the terms: -0.681818182 + x = -2.025151765 Solving -0.681818182 + x = -2.025151765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.681818182' to each side of the equation. -0.681818182 + 0.681818182 + x = -2.025151765 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + x = -2.025151765 + 0.681818182 x = -2.025151765 + 0.681818182 Combine like terms: -2.025151765 + 0.681818182 = -1.343333583 x = -1.343333583 Simplifying x = -1.343333583Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.706969947, -1.343333583}
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