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Simplifying 16x2 + 13x + -28 = 0 Reorder the terms: -28 + 13x + 16x2 = 0 Solving -28 + 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'. -1.75 + 0.8125x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 0.8125x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 0.8125x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 0.8125x + x2 = 0 + 1.75 0.8125x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 0.8125x + x2 = 1.75 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 = 1.75 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125x + x2 = 1.75 + 0.1650390625 Combine like terms: 1.75 + 0.1650390625 = 1.9150390625 0.1650390625 + 0.8125x + x2 = 1.9150390625 Factor a perfect square on the left side: (x + 0.40625)(x + 0.40625) = 1.9150390625 Calculate the square root of the right side: 1.383849364 Break this problem into two subproblems by setting (x + 0.40625) equal to 1.383849364 and -1.383849364.Subproblem 1
x + 0.40625 = 1.383849364 Simplifying x + 0.40625 = 1.383849364 Reorder the terms: 0.40625 + x = 1.383849364 Solving 0.40625 + x = 1.383849364 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 = 1.383849364 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + x = 1.383849364 + -0.40625 x = 1.383849364 + -0.40625 Combine like terms: 1.383849364 + -0.40625 = 0.977599364 x = 0.977599364 Simplifying x = 0.977599364Subproblem 2
x + 0.40625 = -1.383849364 Simplifying x + 0.40625 = -1.383849364 Reorder the terms: 0.40625 + x = -1.383849364 Solving 0.40625 + x = -1.383849364 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 = -1.383849364 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + x = -1.383849364 + -0.40625 x = -1.383849364 + -0.40625 Combine like terms: -1.383849364 + -0.40625 = -1.790099364 x = -1.790099364 Simplifying x = -1.790099364Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.977599364, -1.790099364}
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