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Simplifying 1.25x2 + -9x + -16 = 0 Reorder the terms: -16 + -9x + 1.25x2 = 0 Solving -16 + -9x + 1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -12.8 + -7.2x + x2 = 0 Move the constant term to the right: Add '12.8' to each side of the equation. -12.8 + -7.2x + 12.8 + x2 = 0 + 12.8 Reorder the terms: -12.8 + 12.8 + -7.2x + x2 = 0 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + -7.2x + x2 = 0 + 12.8 -7.2x + x2 = 0 + 12.8 Combine like terms: 0 + 12.8 = 12.8 -7.2x + x2 = 12.8 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = 12.8 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 12.8 + 12.96 Combine like terms: 12.8 + 12.96 = 25.76 12.96 + -7.2x + x2 = 25.76 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 25.76 Calculate the square root of the right side: 5.075431016 Break this problem into two subproblems by setting (x + -3.6) equal to 5.075431016 and -5.075431016.Subproblem 1
x + -3.6 = 5.075431016 Simplifying x + -3.6 = 5.075431016 Reorder the terms: -3.6 + x = 5.075431016 Solving -3.6 + x = 5.075431016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 5.075431016 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 5.075431016 + 3.6 x = 5.075431016 + 3.6 Combine like terms: 5.075431016 + 3.6 = 8.675431016 x = 8.675431016 Simplifying x = 8.675431016Subproblem 2
x + -3.6 = -5.075431016 Simplifying x + -3.6 = -5.075431016 Reorder the terms: -3.6 + x = -5.075431016 Solving -3.6 + x = -5.075431016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -5.075431016 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -5.075431016 + 3.6 x = -5.075431016 + 3.6 Combine like terms: -5.075431016 + 3.6 = -1.475431016 x = -1.475431016 Simplifying x = -1.475431016Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.675431016, -1.475431016}
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