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Simplifying 25x2 + 7x + -6500 = 0 Reorder the terms: -6500 + 7x + 25x2 = 0 Solving -6500 + 7x + 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'. -260 + 0.28x + x2 = 0 Move the constant term to the right: Add '260' to each side of the equation. -260 + 0.28x + 260 + x2 = 0 + 260 Reorder the terms: -260 + 260 + 0.28x + x2 = 0 + 260 Combine like terms: -260 + 260 = 0 0 + 0.28x + x2 = 0 + 260 0.28x + x2 = 0 + 260 Combine like terms: 0 + 260 = 260 0.28x + x2 = 260 The x term is 0.28x. Take half its coefficient (0.14). Square it (0.0196) and add it to both sides. Add '0.0196' to each side of the equation. 0.28x + 0.0196 + x2 = 260 + 0.0196 Reorder the terms: 0.0196 + 0.28x + x2 = 260 + 0.0196 Combine like terms: 260 + 0.0196 = 260.0196 0.0196 + 0.28x + x2 = 260.0196 Factor a perfect square on the left side: (x + 0.14)(x + 0.14) = 260.0196 Calculate the square root of the right side: 16.125123255 Break this problem into two subproblems by setting (x + 0.14) equal to 16.125123255 and -16.125123255.Subproblem 1
x + 0.14 = 16.125123255 Simplifying x + 0.14 = 16.125123255 Reorder the terms: 0.14 + x = 16.125123255 Solving 0.14 + x = 16.125123255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.14' to each side of the equation. 0.14 + -0.14 + x = 16.125123255 + -0.14 Combine like terms: 0.14 + -0.14 = 0.00 0.00 + x = 16.125123255 + -0.14 x = 16.125123255 + -0.14 Combine like terms: 16.125123255 + -0.14 = 15.985123255 x = 15.985123255 Simplifying x = 15.985123255Subproblem 2
x + 0.14 = -16.125123255 Simplifying x + 0.14 = -16.125123255 Reorder the terms: 0.14 + x = -16.125123255 Solving 0.14 + x = -16.125123255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.14' to each side of the equation. 0.14 + -0.14 + x = -16.125123255 + -0.14 Combine like terms: 0.14 + -0.14 = 0.00 0.00 + x = -16.125123255 + -0.14 x = -16.125123255 + -0.14 Combine like terms: -16.125123255 + -0.14 = -16.265123255 x = -16.265123255 Simplifying x = -16.265123255Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.985123255, -16.265123255}
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