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Simplifying 215 = 16x2 + 32x Reorder the terms: 215 = 32x + 16x2 Solving 215 = 32x + 16x2 Solving for variable 'x'. Reorder the terms: 215 + -32x + -16x2 = 32x + -32x + 16x2 + -16x2 Combine like terms: 32x + -32x = 0 215 + -32x + -16x2 = 0 + 16x2 + -16x2 215 + -32x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 215 + -32x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -13.4375 + 2x + x2 = 0 Move the constant term to the right: Add '13.4375' to each side of the equation. -13.4375 + 2x + 13.4375 + x2 = 0 + 13.4375 Reorder the terms: -13.4375 + 13.4375 + 2x + x2 = 0 + 13.4375 Combine like terms: -13.4375 + 13.4375 = 0.0000 0.0000 + 2x + x2 = 0 + 13.4375 2x + x2 = 0 + 13.4375 Combine like terms: 0 + 13.4375 = 13.4375 2x + x2 = 13.4375 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 13.4375 + 1 Reorder the terms: 1 + 2x + x2 = 13.4375 + 1 Combine like terms: 13.4375 + 1 = 14.4375 1 + 2x + x2 = 14.4375 Factor a perfect square on the left side: (x + 1)(x + 1) = 14.4375 Calculate the square root of the right side: 3.799671038 Break this problem into two subproblems by setting (x + 1) equal to 3.799671038 and -3.799671038.Subproblem 1
x + 1 = 3.799671038 Simplifying x + 1 = 3.799671038 Reorder the terms: 1 + x = 3.799671038 Solving 1 + x = 3.799671038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.799671038 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.799671038 + -1 x = 3.799671038 + -1 Combine like terms: 3.799671038 + -1 = 2.799671038 x = 2.799671038 Simplifying x = 2.799671038Subproblem 2
x + 1 = -3.799671038 Simplifying x + 1 = -3.799671038 Reorder the terms: 1 + x = -3.799671038 Solving 1 + x = -3.799671038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.799671038 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.799671038 + -1 x = -3.799671038 + -1 Combine like terms: -3.799671038 + -1 = -4.799671038 x = -4.799671038 Simplifying x = -4.799671038Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.799671038, -4.799671038}
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