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Simplifying 2x2 + 12x = 21 Reorder the terms: 12x + 2x2 = 21 Solving 12x + 2x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 12x + 2x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 6x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 6x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 6x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 6x + x2 = 0 + 10.5 6x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 6x + x2 = 10.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 10.5 + 9 Reorder the terms: 9 + 6x + x2 = 10.5 + 9 Combine like terms: 10.5 + 9 = 19.5 9 + 6x + x2 = 19.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (x + 3) equal to 4.415880433 and -4.415880433.Subproblem 1
x + 3 = 4.415880433 Simplifying x + 3 = 4.415880433 Reorder the terms: 3 + x = 4.415880433 Solving 3 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.415880433 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.415880433 + -3 x = 4.415880433 + -3 Combine like terms: 4.415880433 + -3 = 1.415880433 x = 1.415880433 Simplifying x = 1.415880433Subproblem 2
x + 3 = -4.415880433 Simplifying x + 3 = -4.415880433 Reorder the terms: 3 + x = -4.415880433 Solving 3 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.415880433 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.415880433 + -3 x = -4.415880433 + -3 Combine like terms: -4.415880433 + -3 = -7.415880433 x = -7.415880433 Simplifying x = -7.415880433Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.415880433, -7.415880433}
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