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Simplifying 8x2 + 40x = -25 Reorder the terms: 40x + 8x2 = -25 Solving 40x + 8x2 = -25 Solving for variable 'x'. Reorder the terms: 25 + 40x + 8x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 40x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.125 + 5x + x2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + 5x + -3.125 + x2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + 5x + x2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + 5x + x2 = 0 + -3.125 5x + x2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 5x + x2 = -3.125 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -3.125 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -3.125 + 6.25 Combine like terms: -3.125 + 6.25 = 3.125 6.25 + 5x + x2 = 3.125 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (x + 2.5) equal to 1.767766953 and -1.767766953.Subproblem 1
x + 2.5 = 1.767766953 Simplifying x + 2.5 = 1.767766953 Reorder the terms: 2.5 + x = 1.767766953 Solving 2.5 + x = 1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.767766953 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.767766953 + -2.5 x = 1.767766953 + -2.5 Combine like terms: 1.767766953 + -2.5 = -0.732233047 x = -0.732233047 Simplifying x = -0.732233047Subproblem 2
x + 2.5 = -1.767766953 Simplifying x + 2.5 = -1.767766953 Reorder the terms: 2.5 + x = -1.767766953 Solving 2.5 + x = -1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.767766953 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.767766953 + -2.5 x = -1.767766953 + -2.5 Combine like terms: -1.767766953 + -2.5 = -4.267766953 x = -4.267766953 Simplifying x = -4.267766953Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.732233047, -4.267766953}
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