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Simplifying -16x2 + 20x + -3 = 0 Reorder the terms: -3 + 20x + -16x2 = 0 Solving -3 + 20x + -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'. 0.1875 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -1.25x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -1.25x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -1.25x + x2 = 0 + -0.1875 -1.25x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -1.25x + x2 = -0.1875 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.1875 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.1875 + 0.390625 Combine like terms: -0.1875 + 0.390625 = 0.203125 0.390625 + -1.25x + x2 = 0.203125 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.203125 Calculate the square root of the right side: 0.450693909 Break this problem into two subproblems by setting (x + -0.625) equal to 0.450693909 and -0.450693909.Subproblem 1
x + -0.625 = 0.450693909 Simplifying x + -0.625 = 0.450693909 Reorder the terms: -0.625 + x = 0.450693909 Solving -0.625 + x = 0.450693909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.450693909 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.450693909 + 0.625 x = 0.450693909 + 0.625 Combine like terms: 0.450693909 + 0.625 = 1.075693909 x = 1.075693909 Simplifying x = 1.075693909Subproblem 2
x + -0.625 = -0.450693909 Simplifying x + -0.625 = -0.450693909 Reorder the terms: -0.625 + x = -0.450693909 Solving -0.625 + x = -0.450693909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.450693909 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.450693909 + 0.625 x = -0.450693909 + 0.625 Combine like terms: -0.450693909 + 0.625 = 0.174306091 x = 0.174306091 Simplifying x = 0.174306091Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.075693909, 0.174306091}
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