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Simplifying 4x2 + -64x + -25 = 0 Reorder the terms: -25 + -64x + 4x2 = 0 Solving -25 + -64x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -16x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -16x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -16x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -16x + x2 = 0 + 6.25 -16x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -16x + x2 = 6.25 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 6.25 + 64 Reorder the terms: 64 + -16x + x2 = 6.25 + 64 Combine like terms: 6.25 + 64 = 70.25 64 + -16x + x2 = 70.25 Factor a perfect square on the left side: (x + -8)(x + -8) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x + -8) equal to 8.381527307 and -8.381527307.Subproblem 1
x + -8 = 8.381527307 Simplifying x + -8 = 8.381527307 Reorder the terms: -8 + x = 8.381527307 Solving -8 + x = 8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 8.381527307 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.381527307 + 8 x = 8.381527307 + 8 Combine like terms: 8.381527307 + 8 = 16.381527307 x = 16.381527307 Simplifying x = 16.381527307Subproblem 2
x + -8 = -8.381527307 Simplifying x + -8 = -8.381527307 Reorder the terms: -8 + x = -8.381527307 Solving -8 + x = -8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -8.381527307 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.381527307 + 8 x = -8.381527307 + 8 Combine like terms: -8.381527307 + 8 = -0.381527307 x = -0.381527307 Simplifying x = -0.381527307Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.381527307, -0.381527307}
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