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Simplifying 34 = 5x + 16x2 Solving 34 = 5x + 16x2 Solving for variable 'x'. Reorder the terms: 34 + -5x + -16x2 = 5x + -5x + 16x2 + -16x2 Combine like terms: 5x + -5x = 0 34 + -5x + -16x2 = 0 + 16x2 + -16x2 34 + -5x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 34 + -5x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.125 + 0.3125x + x2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + 0.3125x + 2.125 + x2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + 0.3125x + x2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + 0.3125x + x2 = 0 + 2.125 0.3125x + x2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 0.3125x + x2 = 2.125 The x term is 0.3125x. Take half its coefficient (0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. 0.3125x + 0.0244140625 + x2 = 2.125 + 0.0244140625 Reorder the terms: 0.0244140625 + 0.3125x + x2 = 2.125 + 0.0244140625 Combine like terms: 2.125 + 0.0244140625 = 2.1494140625 0.0244140625 + 0.3125x + x2 = 2.1494140625 Factor a perfect square on the left side: (x + 0.15625)(x + 0.15625) = 2.1494140625 Calculate the square root of the right side: 1.466088013 Break this problem into two subproblems by setting (x + 0.15625) equal to 1.466088013 and -1.466088013.Subproblem 1
x + 0.15625 = 1.466088013 Simplifying x + 0.15625 = 1.466088013 Reorder the terms: 0.15625 + x = 1.466088013 Solving 0.15625 + x = 1.466088013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = 1.466088013 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = 1.466088013 + -0.15625 x = 1.466088013 + -0.15625 Combine like terms: 1.466088013 + -0.15625 = 1.309838013 x = 1.309838013 Simplifying x = 1.309838013Subproblem 2
x + 0.15625 = -1.466088013 Simplifying x + 0.15625 = -1.466088013 Reorder the terms: 0.15625 + x = -1.466088013 Solving 0.15625 + x = -1.466088013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = -1.466088013 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = -1.466088013 + -0.15625 x = -1.466088013 + -0.15625 Combine like terms: -1.466088013 + -0.15625 = -1.622338013 x = -1.622338013 Simplifying x = -1.622338013Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.309838013, -1.622338013}
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