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Simplifying 3x2 + 7x + -162 = 0 Reorder the terms: -162 + 7x + 3x2 = 0 Solving -162 + 7x + 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'. -54 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 2.333333333x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 2.333333333x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 2.333333333x + x2 = 0 + 54 2.333333333x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 2.333333333x + x2 = 54 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 54 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 54 + 1.361111112 Combine like terms: 54 + 1.361111112 = 55.361111112 1.361111112 + 2.333333333x + x2 = 55.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 55.361111112 Calculate the square root of the right side: 7.440504762 Break this problem into two subproblems by setting (x + 1.166666667) equal to 7.440504762 and -7.440504762.Subproblem 1
x + 1.166666667 = 7.440504762 Simplifying x + 1.166666667 = 7.440504762 Reorder the terms: 1.166666667 + x = 7.440504762 Solving 1.166666667 + x = 7.440504762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 7.440504762 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 7.440504762 + -1.166666667 x = 7.440504762 + -1.166666667 Combine like terms: 7.440504762 + -1.166666667 = 6.273838095 x = 6.273838095 Simplifying x = 6.273838095Subproblem 2
x + 1.166666667 = -7.440504762 Simplifying x + 1.166666667 = -7.440504762 Reorder the terms: 1.166666667 + x = -7.440504762 Solving 1.166666667 + x = -7.440504762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -7.440504762 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -7.440504762 + -1.166666667 x = -7.440504762 + -1.166666667 Combine like terms: -7.440504762 + -1.166666667 = -8.607171429 x = -8.607171429 Simplifying x = -8.607171429Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.273838095, -8.607171429}
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