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Simplifying 3x2 + 21x + -6.9 = 0 Reorder the terms: -6.9 + 21x + 3x2 = 0 Solving -6.9 + 21x + 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'. -2.3 + 7x + x2 = 0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + 7x + 2.3 + x2 = 0 + 2.3 Reorder the terms: -2.3 + 2.3 + 7x + x2 = 0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + 7x + x2 = 0 + 2.3 7x + x2 = 0 + 2.3 Combine like terms: 0 + 2.3 = 2.3 7x + x2 = 2.3 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 = 2.3 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 2.3 + 12.25 Combine like terms: 2.3 + 12.25 = 14.55 12.25 + 7x + x2 = 14.55 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 14.55 Calculate the square root of the right side: 3.814446225 Break this problem into two subproblems by setting (x + 3.5) equal to 3.814446225 and -3.814446225.Subproblem 1
x + 3.5 = 3.814446225 Simplifying x + 3.5 = 3.814446225 Reorder the terms: 3.5 + x = 3.814446225 Solving 3.5 + x = 3.814446225 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 = 3.814446225 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.814446225 + -3.5 x = 3.814446225 + -3.5 Combine like terms: 3.814446225 + -3.5 = 0.314446225 x = 0.314446225 Simplifying x = 0.314446225Subproblem 2
x + 3.5 = -3.814446225 Simplifying x + 3.5 = -3.814446225 Reorder the terms: 3.5 + x = -3.814446225 Solving 3.5 + x = -3.814446225 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 = -3.814446225 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.814446225 + -3.5 x = -3.814446225 + -3.5 Combine like terms: -3.814446225 + -3.5 = -7.314446225 x = -7.314446225 Simplifying x = -7.314446225Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.314446225, -7.314446225}
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