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Simplifying x2 = -4(4x + 1) Reorder the terms: x2 = -4(1 + 4x) x2 = (1 * -4 + 4x * -4) x2 = (-4 + -16x) Solving x2 = -4 + -16x Solving for variable 'x'. Reorder the terms: 4 + 16x + x2 = -4 + -16x + 4 + 16x Reorder the terms: 4 + 16x + x2 = -4 + 4 + -16x + 16x Combine like terms: -4 + 4 = 0 4 + 16x + x2 = 0 + -16x + 16x 4 + 16x + x2 = -16x + 16x Combine like terms: -16x + 16x = 0 4 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 16x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 16x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 16x + x2 = 0 + -4 16x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 16x + x2 = -4 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 = -4 + 64 Reorder the terms: 64 + 16x + x2 = -4 + 64 Combine like terms: -4 + 64 = 60 64 + 16x + x2 = 60 Factor a perfect square on the left side: (x + 8)(x + 8) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 8) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 8 = 7.745966692 Simplifying x + 8 = 7.745966692 Reorder the terms: 8 + x = 7.745966692 Solving 8 + x = 7.745966692 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 = 7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.745966692 + -8 x = 7.745966692 + -8 Combine like terms: 7.745966692 + -8 = -0.254033308 x = -0.254033308 Simplifying x = -0.254033308Subproblem 2
x + 8 = -7.745966692 Simplifying x + 8 = -7.745966692 Reorder the terms: 8 + x = -7.745966692 Solving 8 + x = -7.745966692 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 = -7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.745966692 + -8 x = -7.745966692 + -8 Combine like terms: -7.745966692 + -8 = -15.745966692 x = -15.745966692 Simplifying x = -15.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.254033308, -15.745966692}
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