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Simplifying 25x2 + 7x + -96 = 0 Reorder the terms: -96 + 7x + 25x2 = 0 Solving -96 + 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'. -3.84 + 0.28x + x2 = 0 Move the constant term to the right: Add '3.84' to each side of the equation. -3.84 + 0.28x + 3.84 + x2 = 0 + 3.84 Reorder the terms: -3.84 + 3.84 + 0.28x + x2 = 0 + 3.84 Combine like terms: -3.84 + 3.84 = 0.00 0.00 + 0.28x + x2 = 0 + 3.84 0.28x + x2 = 0 + 3.84 Combine like terms: 0 + 3.84 = 3.84 0.28x + x2 = 3.84 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 = 3.84 + 0.0196 Reorder the terms: 0.0196 + 0.28x + x2 = 3.84 + 0.0196 Combine like terms: 3.84 + 0.0196 = 3.8596 0.0196 + 0.28x + x2 = 3.8596 Factor a perfect square on the left side: (x + 0.14)(x + 0.14) = 3.8596 Calculate the square root of the right side: 1.96458647 Break this problem into two subproblems by setting (x + 0.14) equal to 1.96458647 and -1.96458647.Subproblem 1
x + 0.14 = 1.96458647 Simplifying x + 0.14 = 1.96458647 Reorder the terms: 0.14 + x = 1.96458647 Solving 0.14 + x = 1.96458647 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 = 1.96458647 + -0.14 Combine like terms: 0.14 + -0.14 = 0.00 0.00 + x = 1.96458647 + -0.14 x = 1.96458647 + -0.14 Combine like terms: 1.96458647 + -0.14 = 1.82458647 x = 1.82458647 Simplifying x = 1.82458647Subproblem 2
x + 0.14 = -1.96458647 Simplifying x + 0.14 = -1.96458647 Reorder the terms: 0.14 + x = -1.96458647 Solving 0.14 + x = -1.96458647 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 = -1.96458647 + -0.14 Combine like terms: 0.14 + -0.14 = 0.00 0.00 + x = -1.96458647 + -0.14 x = -1.96458647 + -0.14 Combine like terms: -1.96458647 + -0.14 = -2.10458647 x = -2.10458647 Simplifying x = -2.10458647Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.82458647, -2.10458647}
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