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Simplifying x2 + 32x = 54 Reorder the terms: 32x + x2 = 54 Solving 32x + x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 32x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 32x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 32x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 32x + x2 = 0 + 54 32x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 32x + x2 = 54 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 = 54 + 256 Reorder the terms: 256 + 32x + x2 = 54 + 256 Combine like terms: 54 + 256 = 310 256 + 32x + x2 = 310 Factor a perfect square on the left side: (x + 16)(x + 16) = 310 Calculate the square root of the right side: 17.606816862 Break this problem into two subproblems by setting (x + 16) equal to 17.606816862 and -17.606816862.Subproblem 1
x + 16 = 17.606816862 Simplifying x + 16 = 17.606816862 Reorder the terms: 16 + x = 17.606816862 Solving 16 + x = 17.606816862 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 = 17.606816862 + -16 Combine like terms: 16 + -16 = 0 0 + x = 17.606816862 + -16 x = 17.606816862 + -16 Combine like terms: 17.606816862 + -16 = 1.606816862 x = 1.606816862 Simplifying x = 1.606816862Subproblem 2
x + 16 = -17.606816862 Simplifying x + 16 = -17.606816862 Reorder the terms: 16 + x = -17.606816862 Solving 16 + x = -17.606816862 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 = -17.606816862 + -16 Combine like terms: 16 + -16 = 0 0 + x = -17.606816862 + -16 x = -17.606816862 + -16 Combine like terms: -17.606816862 + -16 = -33.606816862 x = -33.606816862 Simplifying x = -33.606816862Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.606816862, -33.606816862}
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