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Simplifying 0 = x2 + -21.75x + 15.75 Reorder the terms: 0 = 15.75 + -21.75x + x2 Solving 0 = 15.75 + -21.75x + x2 Solving for variable 'x'. Combine like terms: 0 + -15.75 = -15.75 -15.75 + 21.75x + -1x2 = 15.75 + -21.75x + x2 + -15.75 + 21.75x + -1x2 Reorder the terms: -15.75 + 21.75x + -1x2 = 15.75 + -15.75 + -21.75x + 21.75x + x2 + -1x2 Combine like terms: 15.75 + -15.75 = 0.00 -15.75 + 21.75x + -1x2 = 0.00 + -21.75x + 21.75x + x2 + -1x2 -15.75 + 21.75x + -1x2 = -21.75x + 21.75x + x2 + -1x2 Combine like terms: -21.75x + 21.75x = 0.00 -15.75 + 21.75x + -1x2 = 0.00 + x2 + -1x2 -15.75 + 21.75x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15.75 + 21.75x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 15.75 + -21.75x + x2 = 0 Move the constant term to the right: Add '-15.75' to each side of the equation. 15.75 + -21.75x + -15.75 + x2 = 0 + -15.75 Reorder the terms: 15.75 + -15.75 + -21.75x + x2 = 0 + -15.75 Combine like terms: 15.75 + -15.75 = 0.00 0.00 + -21.75x + x2 = 0 + -15.75 -21.75x + x2 = 0 + -15.75 Combine like terms: 0 + -15.75 = -15.75 -21.75x + x2 = -15.75 The x term is -21.75x. Take half its coefficient (-10.875). Square it (118.265625) and add it to both sides. Add '118.265625' to each side of the equation. -21.75x + 118.265625 + x2 = -15.75 + 118.265625 Reorder the terms: 118.265625 + -21.75x + x2 = -15.75 + 118.265625 Combine like terms: -15.75 + 118.265625 = 102.515625 118.265625 + -21.75x + x2 = 102.515625 Factor a perfect square on the left side: (x + -10.875)(x + -10.875) = 102.515625 Calculate the square root of the right side: 10.125 Break this problem into two subproblems by setting (x + -10.875) equal to 10.125 and -10.125.Subproblem 1
x + -10.875 = 10.125 Simplifying x + -10.875 = 10.125 Reorder the terms: -10.875 + x = 10.125 Solving -10.875 + x = 10.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.875' to each side of the equation. -10.875 + 10.875 + x = 10.125 + 10.875 Combine like terms: -10.875 + 10.875 = 0.000 0.000 + x = 10.125 + 10.875 x = 10.125 + 10.875 Combine like terms: 10.125 + 10.875 = 21 x = 21 Simplifying x = 21Subproblem 2
x + -10.875 = -10.125 Simplifying x + -10.875 = -10.125 Reorder the terms: -10.875 + x = -10.125 Solving -10.875 + x = -10.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.875' to each side of the equation. -10.875 + 10.875 + x = -10.125 + 10.875 Combine like terms: -10.875 + 10.875 = 0.000 0.000 + x = -10.125 + 10.875 x = -10.125 + 10.875 Combine like terms: -10.125 + 10.875 = 0.75 x = 0.75 Simplifying x = 0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {21, 0.75}
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