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Simplifying 25x2 + -10x + -9 = 0 Reorder the terms: -9 + -10x + 25x2 = 0 Solving -9 + -10x + 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'. -0.36 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + -0.4x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + -0.4x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + -0.4x + x2 = 0 + 0.36 -0.4x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 -0.4x + x2 = 0.36 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.36 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.36 + 0.04 Combine like terms: 0.36 + 0.04 = 0.4 0.04 + -0.4x + x2 = 0.4 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + -0.2) equal to 0.632455532 and -0.632455532.Subproblem 1
x + -0.2 = 0.632455532 Simplifying x + -0.2 = 0.632455532 Reorder the terms: -0.2 + x = 0.632455532 Solving -0.2 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.632455532 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.632455532 + 0.2 x = 0.632455532 + 0.2 Combine like terms: 0.632455532 + 0.2 = 0.832455532 x = 0.832455532 Simplifying x = 0.832455532Subproblem 2
x + -0.2 = -0.632455532 Simplifying x + -0.2 = -0.632455532 Reorder the terms: -0.2 + x = -0.632455532 Solving -0.2 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.632455532 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.632455532 + 0.2 x = -0.632455532 + 0.2 Combine like terms: -0.632455532 + 0.2 = -0.432455532 x = -0.432455532 Simplifying x = -0.432455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.832455532, -0.432455532}
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