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Simplifying -5x2 + -40x + -72 = 0 Reorder the terms: -72 + -40x + -5x2 = 0 Solving -72 + -40x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(72 + 40x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(72 + 40x + 5x2)' equal to zero and attempt to solve: Simplifying 72 + 40x + 5x2 = 0 Solving 72 + 40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 14.4 + 8x + x2 = 0 Move the constant term to the right: Add '-14.4' to each side of the equation. 14.4 + 8x + -14.4 + x2 = 0 + -14.4 Reorder the terms: 14.4 + -14.4 + 8x + x2 = 0 + -14.4 Combine like terms: 14.4 + -14.4 = 0.0 0.0 + 8x + x2 = 0 + -14.4 8x + x2 = 0 + -14.4 Combine like terms: 0 + -14.4 = -14.4 8x + x2 = -14.4 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -14.4 + 16 Reorder the terms: 16 + 8x + x2 = -14.4 + 16 Combine like terms: -14.4 + 16 = 1.6 16 + 8x + x2 = 1.6 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.6 Calculate the square root of the right side: 1.264911064 Break this problem into two subproblems by setting (x + 4) equal to 1.264911064 and -1.264911064.Subproblem 1
x + 4 = 1.264911064 Simplifying x + 4 = 1.264911064 Reorder the terms: 4 + x = 1.264911064 Solving 4 + x = 1.264911064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 1.264911064 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.264911064 + -4 x = 1.264911064 + -4 Combine like terms: 1.264911064 + -4 = -2.735088936 x = -2.735088936 Simplifying x = -2.735088936Subproblem 2
x + 4 = -1.264911064 Simplifying x + 4 = -1.264911064 Reorder the terms: 4 + x = -1.264911064 Solving 4 + x = -1.264911064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -1.264911064 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.264911064 + -4 x = -1.264911064 + -4 Combine like terms: -1.264911064 + -4 = -5.264911064 x = -5.264911064 Simplifying x = -5.264911064Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.735088936, -5.264911064}Solution
x = {-2.735088936, -5.264911064}
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