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Simplifying x2 + 32x + 53 = 0 Reorder the terms: 53 + 32x + x2 = 0 Solving 53 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 32x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 32x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 32x + x2 = 0 + -53 32x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 32x + x2 = -53 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 = -53 + 256 Reorder the terms: 256 + 32x + x2 = -53 + 256 Combine like terms: -53 + 256 = 203 256 + 32x + x2 = 203 Factor a perfect square on the left side: (x + 16)(x + 16) = 203 Calculate the square root of the right side: 14.247806849 Break this problem into two subproblems by setting (x + 16) equal to 14.247806849 and -14.247806849.Subproblem 1
x + 16 = 14.247806849 Simplifying x + 16 = 14.247806849 Reorder the terms: 16 + x = 14.247806849 Solving 16 + x = 14.247806849 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 = 14.247806849 + -16 Combine like terms: 16 + -16 = 0 0 + x = 14.247806849 + -16 x = 14.247806849 + -16 Combine like terms: 14.247806849 + -16 = -1.752193151 x = -1.752193151 Simplifying x = -1.752193151Subproblem 2
x + 16 = -14.247806849 Simplifying x + 16 = -14.247806849 Reorder the terms: 16 + x = -14.247806849 Solving 16 + x = -14.247806849 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 = -14.247806849 + -16 Combine like terms: 16 + -16 = 0 0 + x = -14.247806849 + -16 x = -14.247806849 + -16 Combine like terms: -14.247806849 + -16 = -30.247806849 x = -30.247806849 Simplifying x = -30.247806849Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.752193151, -30.247806849}
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