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Simplifying 25x2 + 45x + -18 = 0 Reorder the terms: -18 + 45x + 25x2 = 0 Solving -18 + 45x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.72 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.72' to each side of the equation. -0.72 + 1.8x + 0.72 + x2 = 0 + 0.72 Reorder the terms: -0.72 + 0.72 + 1.8x + x2 = 0 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + 1.8x + x2 = 0 + 0.72 1.8x + x2 = 0 + 0.72 Combine like terms: 0 + 0.72 = 0.72 1.8x + x2 = 0.72 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.72 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.72 + 0.81 Combine like terms: 0.72 + 0.81 = 1.53 0.81 + 1.8x + x2 = 1.53 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.53 Calculate the square root of the right side: 1.236931688 Break this problem into two subproblems by setting (x + 0.9) equal to 1.236931688 and -1.236931688.Subproblem 1
x + 0.9 = 1.236931688 Simplifying x + 0.9 = 1.236931688 Reorder the terms: 0.9 + x = 1.236931688 Solving 0.9 + x = 1.236931688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.236931688 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.236931688 + -0.9 x = 1.236931688 + -0.9 Combine like terms: 1.236931688 + -0.9 = 0.336931688 x = 0.336931688 Simplifying x = 0.336931688Subproblem 2
x + 0.9 = -1.236931688 Simplifying x + 0.9 = -1.236931688 Reorder the terms: 0.9 + x = -1.236931688 Solving 0.9 + x = -1.236931688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.236931688 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.236931688 + -0.9 x = -1.236931688 + -0.9 Combine like terms: -1.236931688 + -0.9 = -2.136931688 x = -2.136931688 Simplifying x = -2.136931688Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.336931688, -2.136931688}
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