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Simplifying 16x2 + 32x + 13 = 0 Reorder the terms: 13 + 32x + 16x2 = 0 Solving 13 + 32x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.8125 + 2x + x2 = 0 Move the constant term to the right: Add '-0.8125' to each side of the equation. 0.8125 + 2x + -0.8125 + x2 = 0 + -0.8125 Reorder the terms: 0.8125 + -0.8125 + 2x + x2 = 0 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + 2x + x2 = 0 + -0.8125 2x + x2 = 0 + -0.8125 Combine like terms: 0 + -0.8125 = -0.8125 2x + x2 = -0.8125 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 = -0.8125 + 1 Reorder the terms: 1 + 2x + x2 = -0.8125 + 1 Combine like terms: -0.8125 + 1 = 0.1875 1 + 2x + x2 = 0.1875 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (x + 1) equal to 0.433012702 and -0.433012702.Subproblem 1
x + 1 = 0.433012702 Simplifying x + 1 = 0.433012702 Reorder the terms: 1 + x = 0.433012702 Solving 1 + x = 0.433012702 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 = 0.433012702 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.433012702 + -1 x = 0.433012702 + -1 Combine like terms: 0.433012702 + -1 = -0.566987298 x = -0.566987298 Simplifying x = -0.566987298Subproblem 2
x + 1 = -0.433012702 Simplifying x + 1 = -0.433012702 Reorder the terms: 1 + x = -0.433012702 Solving 1 + x = -0.433012702 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 = -0.433012702 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.433012702 + -1 x = -0.433012702 + -1 Combine like terms: -0.433012702 + -1 = -1.433012702 x = -1.433012702 Simplifying x = -1.433012702Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.566987298, -1.433012702}
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