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Simplifying x2 + -4x + -156 = 0 Reorder the terms: -156 + -4x + x2 = 0 Solving -156 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + -4x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + -4x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + -4x + x2 = 0 + 156 -4x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 -4x + x2 = 156 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 156 + 4 Reorder the terms: 4 + -4x + x2 = 156 + 4 Combine like terms: 156 + 4 = 160 4 + -4x + x2 = 160 Factor a perfect square on the left side: (x + -2)(x + -2) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + -2) equal to 12.649110641 and -12.649110641.Subproblem 1
x + -2 = 12.649110641 Simplifying x + -2 = 12.649110641 Reorder the terms: -2 + x = 12.649110641 Solving -2 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 12.649110641 + 2 Combine like terms: -2 + 2 = 0 0 + x = 12.649110641 + 2 x = 12.649110641 + 2 Combine like terms: 12.649110641 + 2 = 14.649110641 x = 14.649110641 Simplifying x = 14.649110641Subproblem 2
x + -2 = -12.649110641 Simplifying x + -2 = -12.649110641 Reorder the terms: -2 + x = -12.649110641 Solving -2 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -12.649110641 + 2 Combine like terms: -2 + 2 = 0 0 + x = -12.649110641 + 2 x = -12.649110641 + 2 Combine like terms: -12.649110641 + 2 = -10.649110641 x = -10.649110641 Simplifying x = -10.649110641Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.649110641, -10.649110641}
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