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Simplifying 4x2 + 28x + -3x + -21 = 98 Reorder the terms: -21 + 28x + -3x + 4x2 = 98 Combine like terms: 28x + -3x = 25x -21 + 25x + 4x2 = 98 Solving -21 + 25x + 4x2 = 98 Solving for variable 'x'. Reorder the terms: -21 + -98 + 25x + 4x2 = 98 + -98 Combine like terms: -21 + -98 = -119 -119 + 25x + 4x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -119 + 25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -29.75 + 6.25x + x2 = 0 Move the constant term to the right: Add '29.75' to each side of the equation. -29.75 + 6.25x + 29.75 + x2 = 0 + 29.75 Reorder the terms: -29.75 + 29.75 + 6.25x + x2 = 0 + 29.75 Combine like terms: -29.75 + 29.75 = 0.00 0.00 + 6.25x + x2 = 0 + 29.75 6.25x + x2 = 0 + 29.75 Combine like terms: 0 + 29.75 = 29.75 6.25x + x2 = 29.75 The x term is 6.25x. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25x + 9.765625 + x2 = 29.75 + 9.765625 Reorder the terms: 9.765625 + 6.25x + x2 = 29.75 + 9.765625 Combine like terms: 29.75 + 9.765625 = 39.515625 9.765625 + 6.25x + x2 = 39.515625 Factor a perfect square on the left side: (x + 3.125)(x + 3.125) = 39.515625 Calculate the square root of the right side: 6.28614548 Break this problem into two subproblems by setting (x + 3.125) equal to 6.28614548 and -6.28614548.Subproblem 1
x + 3.125 = 6.28614548 Simplifying x + 3.125 = 6.28614548 Reorder the terms: 3.125 + x = 6.28614548 Solving 3.125 + x = 6.28614548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = 6.28614548 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 6.28614548 + -3.125 x = 6.28614548 + -3.125 Combine like terms: 6.28614548 + -3.125 = 3.16114548 x = 3.16114548 Simplifying x = 3.16114548Subproblem 2
x + 3.125 = -6.28614548 Simplifying x + 3.125 = -6.28614548 Reorder the terms: 3.125 + x = -6.28614548 Solving 3.125 + x = -6.28614548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = -6.28614548 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -6.28614548 + -3.125 x = -6.28614548 + -3.125 Combine like terms: -6.28614548 + -3.125 = -9.41114548 x = -9.41114548 Simplifying x = -9.41114548Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.16114548, -9.41114548}
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