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Simplifying (7x2 + 2x) + -1(3x + 8) + (-4x2 + 2x + -4) = 0 Reorder the terms: (2x + 7x2) + -1(3x + 8) + (-4x2 + 2x + -4) = 0 Remove parenthesis around (2x + 7x2) 2x + 7x2 + -1(3x + 8) + (-4x2 + 2x + -4) = 0 Reorder the terms: 2x + 7x2 + -1(8 + 3x) + (-4x2 + 2x + -4) = 0 2x + 7x2 + (8 * -1 + 3x * -1) + (-4x2 + 2x + -4) = 0 2x + 7x2 + (-8 + -3x) + (-4x2 + 2x + -4) = 0 Reorder the terms: 2x + 7x2 + -8 + -3x + (-4 + 2x + -4x2) = 0 Remove parenthesis around (-4 + 2x + -4x2) 2x + 7x2 + -8 + -3x + -4 + 2x + -4x2 = 0 Reorder the terms: -8 + -4 + 2x + -3x + 2x + 7x2 + -4x2 = 0 Combine like terms: -8 + -4 = -12 -12 + 2x + -3x + 2x + 7x2 + -4x2 = 0 Combine like terms: 2x + -3x = -1x -12 + -1x + 2x + 7x2 + -4x2 = 0 Combine like terms: -1x + 2x = 1x -12 + 1x + 7x2 + -4x2 = 0 Combine like terms: 7x2 + -4x2 = 3x2 -12 + 1x + 3x2 = 0 Solving -12 + 1x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.3333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.3333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.3333333333x + x2 = 0 + 4 0.3333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.3333333333x + x2 = 4 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 4 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 4 + 0.02777777779 Combine like terms: 4 + 0.02777777779 = 4.02777777779 0.02777777779 + 0.3333333333x + x2 = 4.02777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 4.02777777779 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 2.00693243 and -2.00693243.Subproblem 1
x + 0.1666666667 = 2.00693243 Simplifying x + 0.1666666667 = 2.00693243 Reorder the terms: 0.1666666667 + x = 2.00693243 Solving 0.1666666667 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 2.00693243 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 2.00693243 + -0.1666666667 x = 2.00693243 + -0.1666666667 Combine like terms: 2.00693243 + -0.1666666667 = 1.8402657633 x = 1.8402657633 Simplifying x = 1.8402657633Subproblem 2
x + 0.1666666667 = -2.00693243 Simplifying x + 0.1666666667 = -2.00693243 Reorder the terms: 0.1666666667 + x = -2.00693243 Solving 0.1666666667 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -2.00693243 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -2.00693243 + -0.1666666667 x = -2.00693243 + -0.1666666667 Combine like terms: -2.00693243 + -0.1666666667 = -2.1735990967 x = -2.1735990967 Simplifying x = -2.1735990967Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8402657633, -2.1735990967}
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