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Simplifying 5x2 + -36x + -40 = 0 Reorder the terms: -40 + -36x + 5x2 = 0 Solving -40 + -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'. -8 + -7.2x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -7.2x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -7.2x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7.2x + x2 = 0 + 8 -7.2x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -7.2x + x2 = 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 = 8 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 8 + 12.96 Combine like terms: 8 + 12.96 = 20.96 12.96 + -7.2x + x2 = 20.96 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 20.96 Calculate the square root of the right side: 4.578209257 Break this problem into two subproblems by setting (x + -3.6) equal to 4.578209257 and -4.578209257.Subproblem 1
x + -3.6 = 4.578209257 Simplifying x + -3.6 = 4.578209257 Reorder the terms: -3.6 + x = 4.578209257 Solving -3.6 + x = 4.578209257 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 = 4.578209257 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 4.578209257 + 3.6 x = 4.578209257 + 3.6 Combine like terms: 4.578209257 + 3.6 = 8.178209257 x = 8.178209257 Simplifying x = 8.178209257Subproblem 2
x + -3.6 = -4.578209257 Simplifying x + -3.6 = -4.578209257 Reorder the terms: -3.6 + x = -4.578209257 Solving -3.6 + x = -4.578209257 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 = -4.578209257 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -4.578209257 + 3.6 x = -4.578209257 + 3.6 Combine like terms: -4.578209257 + 3.6 = -0.978209257 x = -0.978209257 Simplifying x = -0.978209257Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.178209257, -0.978209257}
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