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Simplifying 5x2 + 36x + -64 = 0 Reorder the terms: -64 + 36x + 5x2 = 0 Solving -64 + 36x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -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 = 1.475431016 x = 1.475431016 Simplifying x = 1.475431016Subproblem 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 = -8.675431016 x = -8.675431016 Simplifying x = -8.675431016Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.475431016, -8.675431016}
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