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Simplifying 3x2 + 21x + 36 = 4 Reorder the terms: 36 + 21x + 3x2 = 4 Solving 36 + 21x + 3x2 = 4 Solving for variable 'x'. Reorder the terms: 36 + -4 + 21x + 3x2 = 4 + -4 Combine like terms: 36 + -4 = 32 32 + 21x + 3x2 = 4 + -4 Combine like terms: 4 + -4 = 0 32 + 21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.66666667 + 7x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + 7x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + 7x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + 7x + x2 = 0 + -10.66666667 7x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 7x + x2 = -10.66666667 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -10.66666667 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -10.66666667 + 12.25 Combine like terms: -10.66666667 + 12.25 = 1.58333333 12.25 + 7x + x2 = 1.58333333 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 1.58333333 Calculate the square root of the right side: 1.258305738 Break this problem into two subproblems by setting (x + 3.5) equal to 1.258305738 and -1.258305738.Subproblem 1
x + 3.5 = 1.258305738 Simplifying x + 3.5 = 1.258305738 Reorder the terms: 3.5 + x = 1.258305738 Solving 3.5 + x = 1.258305738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 1.258305738 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.258305738 + -3.5 x = 1.258305738 + -3.5 Combine like terms: 1.258305738 + -3.5 = -2.241694262 x = -2.241694262 Simplifying x = -2.241694262Subproblem 2
x + 3.5 = -1.258305738 Simplifying x + 3.5 = -1.258305738 Reorder the terms: 3.5 + x = -1.258305738 Solving 3.5 + x = -1.258305738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -1.258305738 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.258305738 + -3.5 x = -1.258305738 + -3.5 Combine like terms: -1.258305738 + -3.5 = -4.758305738 x = -4.758305738 Simplifying x = -4.758305738Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.241694262, -4.758305738}
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