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Simplifying 2x2 + -13x + -21 = (x + -5) * 2 Reorder the terms: -21 + -13x + 2x2 = (x + -5) * 2 Reorder the terms: -21 + -13x + 2x2 = (-5 + x) * 2 Reorder the terms for easier multiplication: -21 + -13x + 2x2 = 2(-5 + x) -21 + -13x + 2x2 = (-5 * 2 + x * 2) -21 + -13x + 2x2 = (-10 + 2x) Solving -21 + -13x + 2x2 = -10 + 2x Solving for variable 'x'. Reorder the terms: -21 + 10 + -13x + -2x + 2x2 = -10 + 2x + 10 + -2x Combine like terms: -21 + 10 = -11 -11 + -13x + -2x + 2x2 = -10 + 2x + 10 + -2x Combine like terms: -13x + -2x = -15x -11 + -15x + 2x2 = -10 + 2x + 10 + -2x Reorder the terms: -11 + -15x + 2x2 = -10 + 10 + 2x + -2x Combine like terms: -10 + 10 = 0 -11 + -15x + 2x2 = 0 + 2x + -2x -11 + -15x + 2x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -11 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -7.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -7.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -7.5x + x2 = 0 + 5.5 -7.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -7.5x + x2 = 5.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 5.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 5.5 + 14.0625 Combine like terms: 5.5 + 14.0625 = 19.5625 14.0625 + -7.5x + x2 = 19.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (x + -3.75) equal to 4.422951503 and -4.422951503.Subproblem 1
x + -3.75 = 4.422951503 Simplifying x + -3.75 = 4.422951503 Reorder the terms: -3.75 + x = 4.422951503 Solving -3.75 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 4.422951503 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.422951503 + 3.75 x = 4.422951503 + 3.75 Combine like terms: 4.422951503 + 3.75 = 8.172951503 x = 8.172951503 Simplifying x = 8.172951503Subproblem 2
x + -3.75 = -4.422951503 Simplifying x + -3.75 = -4.422951503 Reorder the terms: -3.75 + x = -4.422951503 Solving -3.75 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -4.422951503 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.422951503 + 3.75 x = -4.422951503 + 3.75 Combine like terms: -4.422951503 + 3.75 = -0.672951503 x = -0.672951503 Simplifying x = -0.672951503Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.172951503, -0.672951503}
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