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Simplifying 150 = x2 + 4x + -6 Reorder the terms: 150 = -6 + 4x + x2 Solving 150 = -6 + 4x + x2 Solving for variable 'x'. Combine like terms: 150 + 6 = 156 156 + -4x + -1x2 = -6 + 4x + x2 + 6 + -4x + -1x2 Reorder the terms: 156 + -4x + -1x2 = -6 + 6 + 4x + -4x + x2 + -1x2 Combine like terms: -6 + 6 = 0 156 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 156 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 156 + -4x + -1x2 = 0 + x2 + -1x2 156 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 156 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -156 + 4x + x2 = 0 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 = 10.649110641 x = 10.649110641 Simplifying x = 10.649110641Subproblem 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 = -14.649110641 x = -14.649110641 Simplifying x = -14.649110641Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.649110641, -14.649110641}
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