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Simplifying 25x2 + 15x = 8 Reorder the terms: 15x + 25x2 = 8 Solving 15x + 25x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 15x + 25x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 15x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.32 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.32' to each side of the equation. -0.32 + 0.6x + 0.32 + x2 = 0 + 0.32 Reorder the terms: -0.32 + 0.32 + 0.6x + x2 = 0 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + 0.6x + x2 = 0 + 0.32 0.6x + x2 = 0 + 0.32 Combine like terms: 0 + 0.32 = 0.32 0.6x + x2 = 0.32 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 0.32 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.32 + 0.09 Combine like terms: 0.32 + 0.09 = 0.41 0.09 + 0.6x + x2 = 0.41 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + 0.3) equal to 0.640312424 and -0.640312424.Subproblem 1
x + 0.3 = 0.640312424 Simplifying x + 0.3 = 0.640312424 Reorder the terms: 0.3 + x = 0.640312424 Solving 0.3 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.640312424 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.640312424 + -0.3 x = 0.640312424 + -0.3 Combine like terms: 0.640312424 + -0.3 = 0.340312424 x = 0.340312424 Simplifying x = 0.340312424Subproblem 2
x + 0.3 = -0.640312424 Simplifying x + 0.3 = -0.640312424 Reorder the terms: 0.3 + x = -0.640312424 Solving 0.3 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.640312424 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.640312424 + -0.3 x = -0.640312424 + -0.3 Combine like terms: -0.640312424 + -0.3 = -0.940312424 x = -0.940312424 Simplifying x = -0.940312424Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.340312424, -0.940312424}
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