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Simplifying 4x2 + -25 + -32x + 4 = 0 Reorder the terms: -25 + 4 + -32x + 4x2 = 0 Combine like terms: -25 + 4 = -21 -21 + -32x + 4x2 = 0 Solving -21 + -32x + 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'. -5.25 + -8x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -8x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -8x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -8x + x2 = 0 + 5.25 -8x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -8x + x2 = 5.25 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 5.25 + 16 Reorder the terms: 16 + -8x + x2 = 5.25 + 16 Combine like terms: 5.25 + 16 = 21.25 16 + -8x + x2 = 21.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -4) equal to 4.609772229 and -4.609772229.Subproblem 1
x + -4 = 4.609772229 Simplifying x + -4 = 4.609772229 Reorder the terms: -4 + x = 4.609772229 Solving -4 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.609772229 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.609772229 + 4 x = 4.609772229 + 4 Combine like terms: 4.609772229 + 4 = 8.609772229 x = 8.609772229 Simplifying x = 8.609772229Subproblem 2
x + -4 = -4.609772229 Simplifying x + -4 = -4.609772229 Reorder the terms: -4 + x = -4.609772229 Solving -4 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.609772229 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.609772229 + 4 x = -4.609772229 + 4 Combine like terms: -4.609772229 + 4 = -0.609772229 x = -0.609772229 Simplifying x = -0.609772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.609772229, -0.609772229}
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