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Simplifying 20 = 16x2 + 48x + 5 Reorder the terms: 20 = 5 + 48x + 16x2 Solving 20 = 5 + 48x + 16x2 Solving for variable 'x'. Combine like terms: 20 + -5 = 15 15 + -48x + -16x2 = 5 + 48x + 16x2 + -5 + -48x + -16x2 Reorder the terms: 15 + -48x + -16x2 = 5 + -5 + 48x + -48x + 16x2 + -16x2 Combine like terms: 5 + -5 = 0 15 + -48x + -16x2 = 0 + 48x + -48x + 16x2 + -16x2 15 + -48x + -16x2 = 48x + -48x + 16x2 + -16x2 Combine like terms: 48x + -48x = 0 15 + -48x + -16x2 = 0 + 16x2 + -16x2 15 + -48x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 15 + -48x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.9375 + 3x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + 3x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + 3x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + 3x + x2 = 0 + 0.9375 3x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 3x + x2 = 0.9375 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.9375 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.9375 + 2.25 Combine like terms: 0.9375 + 2.25 = 3.1875 2.25 + 3x + x2 = 3.1875 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.1875 Calculate the square root of the right side: 1.785357107 Break this problem into two subproblems by setting (x + 1.5) equal to 1.785357107 and -1.785357107.Subproblem 1
x + 1.5 = 1.785357107 Simplifying x + 1.5 = 1.785357107 Reorder the terms: 1.5 + x = 1.785357107 Solving 1.5 + x = 1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.785357107 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.785357107 + -1.5 x = 1.785357107 + -1.5 Combine like terms: 1.785357107 + -1.5 = 0.285357107 x = 0.285357107 Simplifying x = 0.285357107Subproblem 2
x + 1.5 = -1.785357107 Simplifying x + 1.5 = -1.785357107 Reorder the terms: 1.5 + x = -1.785357107 Solving 1.5 + x = -1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.785357107 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.785357107 + -1.5 x = -1.785357107 + -1.5 Combine like terms: -1.785357107 + -1.5 = -3.285357107 x = -3.285357107 Simplifying x = -3.285357107Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.285357107, -3.285357107}
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