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Simplifying 3x2 + 5x + 2 = 145 Reorder the terms: 2 + 5x + 3x2 = 145 Solving 2 + 5x + 3x2 = 145 Solving for variable 'x'. Reorder the terms: 2 + -145 + 5x + 3x2 = 145 + -145 Combine like terms: 2 + -145 = -143 -143 + 5x + 3x2 = 145 + -145 Combine like terms: 145 + -145 = 0 -143 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -47.66666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '47.66666667' to each side of the equation. -47.66666667 + 1.666666667x + 47.66666667 + x2 = 0 + 47.66666667 Reorder the terms: -47.66666667 + 47.66666667 + 1.666666667x + x2 = 0 + 47.66666667 Combine like terms: -47.66666667 + 47.66666667 = 0.00000000 0.00000000 + 1.666666667x + x2 = 0 + 47.66666667 1.666666667x + x2 = 0 + 47.66666667 Combine like terms: 0 + 47.66666667 = 47.66666667 1.666666667x + x2 = 47.66666667 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 47.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 47.66666667 + 0.6944444447 Combine like terms: 47.66666667 + 0.6944444447 = 48.3611111147 0.6944444447 + 1.666666667x + x2 = 48.3611111147 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 48.3611111147 Calculate the square root of the right side: 6.954215349 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 6.954215349 and -6.954215349.Subproblem 1
x + 0.8333333335 = 6.954215349 Simplifying x + 0.8333333335 = 6.954215349 Reorder the terms: 0.8333333335 + x = 6.954215349 Solving 0.8333333335 + x = 6.954215349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 6.954215349 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 6.954215349 + -0.8333333335 x = 6.954215349 + -0.8333333335 Combine like terms: 6.954215349 + -0.8333333335 = 6.1208820155 x = 6.1208820155 Simplifying x = 6.1208820155Subproblem 2
x + 0.8333333335 = -6.954215349 Simplifying x + 0.8333333335 = -6.954215349 Reorder the terms: 0.8333333335 + x = -6.954215349 Solving 0.8333333335 + x = -6.954215349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -6.954215349 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -6.954215349 + -0.8333333335 x = -6.954215349 + -0.8333333335 Combine like terms: -6.954215349 + -0.8333333335 = -7.7875486825 x = -7.7875486825 Simplifying x = -7.7875486825Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.1208820155, -7.7875486825}
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