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Simplifying 0 = 2x2 + x + -25 Reorder the terms: 0 = -25 + x + 2x2 Solving 0 = -25 + x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + -1x + -2x2 = -25 + x + 2x2 + 25 + -1x + -2x2 Reorder the terms: 25 + -1x + -2x2 = -25 + 25 + x + -1x + 2x2 + -2x2 Combine like terms: -25 + 25 = 0 25 + -1x + -2x2 = 0 + x + -1x + 2x2 + -2x2 25 + -1x + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 25 + -1x + -2x2 = 0 + 2x2 + -2x2 25 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 25 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 0.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 0.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 0.5x + x2 = 0 + 12.5 0.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 0.5x + x2 = 12.5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 12.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 12.5 + 0.0625 Combine like terms: 12.5 + 0.0625 = 12.5625 0.0625 + 0.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 0.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 0.25 = 3.54436172 Simplifying x + 0.25 = 3.54436172 Reorder the terms: 0.25 + x = 3.54436172 Solving 0.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.54436172 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.54436172 + -0.25 x = 3.54436172 + -0.25 Combine like terms: 3.54436172 + -0.25 = 3.29436172 x = 3.29436172 Simplifying x = 3.29436172Subproblem 2
x + 0.25 = -3.54436172 Simplifying x + 0.25 = -3.54436172 Reorder the terms: 0.25 + x = -3.54436172 Solving 0.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.54436172 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.54436172 + -0.25 x = -3.54436172 + -0.25 Combine like terms: -3.54436172 + -0.25 = -3.79436172 x = -3.79436172 Simplifying x = -3.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.29436172, -3.79436172}
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