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Simplifying 16x2 + 16x + -59 = 0 Reorder the terms: -59 + 16x + 16x2 = 0 Solving -59 + 16x + 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'. -3.6875 + x + x2 = 0 Move the constant term to the right: Add '3.6875' to each side of the equation. -3.6875 + x + 3.6875 + x2 = 0 + 3.6875 Reorder the terms: -3.6875 + 3.6875 + x + x2 = 0 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x + x2 = 0 + 3.6875 x + x2 = 0 + 3.6875 Combine like terms: 0 + 3.6875 = 3.6875 x + x2 = 3.6875 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 3.6875 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 3.6875 + 0.25 Combine like terms: 3.6875 + 0.25 = 3.9375 1.25 + x2 = 3.9375 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.9375 Calculate the square root of the right side: 1.984313483 Break this problem into two subproblems by setting (x + 0.5) equal to 1.984313483 and -1.984313483.Subproblem 1
x + 0.5 = 1.984313483 Simplifying x + 0.5 = 1.984313483 Reorder the terms: 0.5 + x = 1.984313483 Solving 0.5 + x = 1.984313483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.984313483 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.984313483 + -0.5 x = 1.984313483 + -0.5 Combine like terms: 1.984313483 + -0.5 = 1.484313483 x = 1.484313483 Simplifying x = 1.484313483Subproblem 2
x + 0.5 = -1.984313483 Simplifying x + 0.5 = -1.984313483 Reorder the terms: 0.5 + x = -1.984313483 Solving 0.5 + x = -1.984313483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.984313483 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.984313483 + -0.5 x = -1.984313483 + -0.5 Combine like terms: -1.984313483 + -0.5 = -2.484313483 x = -2.484313483 Simplifying x = -2.484313483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.484313483, -2.484313483}
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