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Simplifying 0 = x2 + -3.5x + -21 Reorder the terms: 0 = -21 + -3.5x + x2 Solving 0 = -21 + -3.5x + x2 Solving for variable 'x'. Combine like terms: 0 + 21 = 21 21 + 3.5x + -1x2 = -21 + -3.5x + x2 + 21 + 3.5x + -1x2 Reorder the terms: 21 + 3.5x + -1x2 = -21 + 21 + -3.5x + 3.5x + x2 + -1x2 Combine like terms: -21 + 21 = 0 21 + 3.5x + -1x2 = 0 + -3.5x + 3.5x + x2 + -1x2 21 + 3.5x + -1x2 = -3.5x + 3.5x + x2 + -1x2 Combine like terms: -3.5x + 3.5x = 0.0 21 + 3.5x + -1x2 = 0.0 + x2 + -1x2 21 + 3.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + 3.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -3.5x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -3.5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -3.5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -3.5x + x2 = 0 + 21 -3.5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -3.5x + x2 = 21 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 21 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 21 + 3.0625 Combine like terms: 21 + 3.0625 = 24.0625 3.0625 + -3.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + -1.75) equal to 4.905354218 and -4.905354218.Subproblem 1
x + -1.75 = 4.905354218 Simplifying x + -1.75 = 4.905354218 Reorder the terms: -1.75 + x = 4.905354218 Solving -1.75 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 4.905354218 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 4.905354218 + 1.75 x = 4.905354218 + 1.75 Combine like terms: 4.905354218 + 1.75 = 6.655354218 x = 6.655354218 Simplifying x = 6.655354218Subproblem 2
x + -1.75 = -4.905354218 Simplifying x + -1.75 = -4.905354218 Reorder the terms: -1.75 + x = -4.905354218 Solving -1.75 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -4.905354218 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -4.905354218 + 1.75 x = -4.905354218 + 1.75 Combine like terms: -4.905354218 + 1.75 = -3.155354218 x = -3.155354218 Simplifying x = -3.155354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.655354218, -3.155354218}
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