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Simplifying 4(x + 4) + 5x(5x) = 161 Reorder the terms: 4(4 + x) + 5x(5x) = 161 (4 * 4 + x * 4) + 5x(5x) = 161 (16 + 4x) + 5x(5x) = 161 Remove parenthesis around (5x) 16 + 4x + 5x * 5x = 161 Reorder the terms for easier multiplication: 16 + 4x + 5 * 5x * x = 161 Multiply 5 * 5 16 + 4x + 25x * x = 161 Multiply x * x 16 + 4x + 25x2 = 161 Solving 16 + 4x + 25x2 = 161 Solving for variable 'x'. Reorder the terms: 16 + -161 + 4x + 25x2 = 161 + -161 Combine like terms: 16 + -161 = -145 -145 + 4x + 25x2 = 161 + -161 Combine like terms: 161 + -161 = 0 -145 + 4x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -5.8 + 0.16x + x2 = 0 Move the constant term to the right: Add '5.8' to each side of the equation. -5.8 + 0.16x + 5.8 + x2 = 0 + 5.8 Reorder the terms: -5.8 + 5.8 + 0.16x + x2 = 0 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + 0.16x + x2 = 0 + 5.8 0.16x + x2 = 0 + 5.8 Combine like terms: 0 + 5.8 = 5.8 0.16x + x2 = 5.8 The x term is 0.16x. Take half its coefficient (0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. 0.16x + 0.0064 + x2 = 5.8 + 0.0064 Reorder the terms: 0.0064 + 0.16x + x2 = 5.8 + 0.0064 Combine like terms: 5.8 + 0.0064 = 5.8064 0.0064 + 0.16x + x2 = 5.8064 Factor a perfect square on the left side: (x + 0.08)(x + 0.08) = 5.8064 Calculate the square root of the right side: 2.409647277 Break this problem into two subproblems by setting (x + 0.08) equal to 2.409647277 and -2.409647277.Subproblem 1
x + 0.08 = 2.409647277 Simplifying x + 0.08 = 2.409647277 Reorder the terms: 0.08 + x = 2.409647277 Solving 0.08 + x = 2.409647277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = 2.409647277 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = 2.409647277 + -0.08 x = 2.409647277 + -0.08 Combine like terms: 2.409647277 + -0.08 = 2.329647277 x = 2.329647277 Simplifying x = 2.329647277Subproblem 2
x + 0.08 = -2.409647277 Simplifying x + 0.08 = -2.409647277 Reorder the terms: 0.08 + x = -2.409647277 Solving 0.08 + x = -2.409647277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = -2.409647277 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = -2.409647277 + -0.08 x = -2.409647277 + -0.08 Combine like terms: -2.409647277 + -0.08 = -2.489647277 x = -2.489647277 Simplifying x = -2.489647277Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.329647277, -2.489647277}
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