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Simplifying 5x2 + 32x + -36 = 0 Reorder the terms: -36 + 32x + 5x2 = 0 Solving -36 + 32x + 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'. -7.2 + 6.4x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 6.4x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 6.4x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 6.4x + x2 = 0 + 7.2 6.4x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 6.4x + x2 = 7.2 The x term is 6.4x. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4x + 10.24 + x2 = 7.2 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = 7.2 + 10.24 Combine like terms: 7.2 + 10.24 = 17.44 10.24 + 6.4x + x2 = 17.44 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 17.44 Calculate the square root of the right side: 4.176122604 Break this problem into two subproblems by setting (x + 3.2) equal to 4.176122604 and -4.176122604.Subproblem 1
x + 3.2 = 4.176122604 Simplifying x + 3.2 = 4.176122604 Reorder the terms: 3.2 + x = 4.176122604 Solving 3.2 + x = 4.176122604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 4.176122604 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 4.176122604 + -3.2 x = 4.176122604 + -3.2 Combine like terms: 4.176122604 + -3.2 = 0.976122604 x = 0.976122604 Simplifying x = 0.976122604Subproblem 2
x + 3.2 = -4.176122604 Simplifying x + 3.2 = -4.176122604 Reorder the terms: 3.2 + x = -4.176122604 Solving 3.2 + x = -4.176122604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -4.176122604 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -4.176122604 + -3.2 x = -4.176122604 + -3.2 Combine like terms: -4.176122604 + -3.2 = -7.376122604 x = -7.376122604 Simplifying x = -7.376122604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.976122604, -7.376122604}
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