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Simplifying 16x2 + -13x + -4 = 0 Reorder the terms: -4 + -13x + 16x2 = 0 Solving -4 + -13x + 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'. -0.25 + -0.8125x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.8125x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.8125x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.8125x + x2 = 0 + 0.25 -0.8125x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.8125x + x2 = 0.25 The x term is -0.8125x. Take half its coefficient (-0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. -0.8125x + 0.1650390625 + x2 = 0.25 + 0.1650390625 Reorder the terms: 0.1650390625 + -0.8125x + x2 = 0.25 + 0.1650390625 Combine like terms: 0.25 + 0.1650390625 = 0.4150390625 0.1650390625 + -0.8125x + x2 = 0.4150390625 Factor a perfect square on the left side: (x + -0.40625)(x + -0.40625) = 0.4150390625 Calculate the square root of the right side: 0.644235254 Break this problem into two subproblems by setting (x + -0.40625) equal to 0.644235254 and -0.644235254.Subproblem 1
x + -0.40625 = 0.644235254 Simplifying x + -0.40625 = 0.644235254 Reorder the terms: -0.40625 + x = 0.644235254 Solving -0.40625 + x = 0.644235254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + x = 0.644235254 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + x = 0.644235254 + 0.40625 x = 0.644235254 + 0.40625 Combine like terms: 0.644235254 + 0.40625 = 1.050485254 x = 1.050485254 Simplifying x = 1.050485254Subproblem 2
x + -0.40625 = -0.644235254 Simplifying x + -0.40625 = -0.644235254 Reorder the terms: -0.40625 + x = -0.644235254 Solving -0.40625 + x = -0.644235254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + x = -0.644235254 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + x = -0.644235254 + 0.40625 x = -0.644235254 + 0.40625 Combine like terms: -0.644235254 + 0.40625 = -0.237985254 x = -0.237985254 Simplifying x = -0.237985254Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.050485254, -0.237985254}
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