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Simplifying 3x(x + 2) + 4 = 5x + 7 Reorder the terms: 3x(2 + x) + 4 = 5x + 7 (2 * 3x + x * 3x) + 4 = 5x + 7 (6x + 3x2) + 4 = 5x + 7 Reorder the terms: 4 + 6x + 3x2 = 5x + 7 Reorder the terms: 4 + 6x + 3x2 = 7 + 5x Solving 4 + 6x + 3x2 = 7 + 5x Solving for variable 'x'. Reorder the terms: 4 + -7 + 6x + -5x + 3x2 = 7 + 5x + -7 + -5x Combine like terms: 4 + -7 = -3 -3 + 6x + -5x + 3x2 = 7 + 5x + -7 + -5x Combine like terms: 6x + -5x = 1x -3 + 1x + 3x2 = 7 + 5x + -7 + -5x Reorder the terms: -3 + 1x + 3x2 = 7 + -7 + 5x + -5x Combine like terms: 7 + -7 = 0 -3 + 1x + 3x2 = 0 + 5x + -5x -3 + 1x + 3x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -3 + 1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.3333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.3333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.3333333333x + x2 = 0 + 1 0.3333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.3333333333x + x2 = 1 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 = 1 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 1 + 0.02777777779 Combine like terms: 1 + 0.02777777779 = 1.02777777779 0.02777777779 + 0.3333333333x + x2 = 1.02777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 1.02777777779 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.013793755 and -1.013793755.Subproblem 1
x + 0.1666666667 = 1.013793755 Simplifying x + 0.1666666667 = 1.013793755 Reorder the terms: 0.1666666667 + x = 1.013793755 Solving 0.1666666667 + x = 1.013793755 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 = 1.013793755 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.013793755 + -0.1666666667 x = 1.013793755 + -0.1666666667 Combine like terms: 1.013793755 + -0.1666666667 = 0.8471270883 x = 0.8471270883 Simplifying x = 0.8471270883Subproblem 2
x + 0.1666666667 = -1.013793755 Simplifying x + 0.1666666667 = -1.013793755 Reorder the terms: 0.1666666667 + x = -1.013793755 Solving 0.1666666667 + x = -1.013793755 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 = -1.013793755 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.013793755 + -0.1666666667 x = -1.013793755 + -0.1666666667 Combine like terms: -1.013793755 + -0.1666666667 = -1.1804604217 x = -1.1804604217 Simplifying x = -1.1804604217Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8471270883, -1.1804604217}
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