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Simplifying x2 + 32x + -150 = 0 Reorder the terms: -150 + 32x + x2 = 0 Solving -150 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 32x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 32x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 32x + x2 = 0 + 150 32x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 32x + x2 = 150 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 150 + 256 Reorder the terms: 256 + 32x + x2 = 150 + 256 Combine like terms: 150 + 256 = 406 256 + 32x + x2 = 406 Factor a perfect square on the left side: (x + 16)(x + 16) = 406 Calculate the square root of the right side: 20.14944168 Break this problem into two subproblems by setting (x + 16) equal to 20.14944168 and -20.14944168.Subproblem 1
x + 16 = 20.14944168 Simplifying x + 16 = 20.14944168 Reorder the terms: 16 + x = 20.14944168 Solving 16 + x = 20.14944168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 20.14944168 + -16 Combine like terms: 16 + -16 = 0 0 + x = 20.14944168 + -16 x = 20.14944168 + -16 Combine like terms: 20.14944168 + -16 = 4.14944168 x = 4.14944168 Simplifying x = 4.14944168Subproblem 2
x + 16 = -20.14944168 Simplifying x + 16 = -20.14944168 Reorder the terms: 16 + x = -20.14944168 Solving 16 + x = -20.14944168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -20.14944168 + -16 Combine like terms: 16 + -16 = 0 0 + x = -20.14944168 + -16 x = -20.14944168 + -16 Combine like terms: -20.14944168 + -16 = -36.14944168 x = -36.14944168 Simplifying x = -36.14944168Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.14944168, -36.14944168}
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