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Simplifying (4x + 5)(x) = 400 Reorder the terms: (5 + 4x)(x) = 400 Reorder the terms for easier multiplication: x(5 + 4x) = 400 (5 * x + 4x * x) = 400 (5x + 4x2) = 400 Solving 5x + 4x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 5x + 4x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -100 + 1.25x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 1.25x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 1.25x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 1.25x + x2 = 0 + 100 1.25x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 1.25x + x2 = 100 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 = 100 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 100 + 0.390625 Combine like terms: 100 + 0.390625 = 100.390625 0.390625 + 1.25x + x2 = 100.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 100.390625 Calculate the square root of the right side: 10.019512214 Break this problem into two subproblems by setting (x + 0.625) equal to 10.019512214 and -10.019512214.Subproblem 1
x + 0.625 = 10.019512214 Simplifying x + 0.625 = 10.019512214 Reorder the terms: 0.625 + x = 10.019512214 Solving 0.625 + x = 10.019512214 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 = 10.019512214 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 10.019512214 + -0.625 x = 10.019512214 + -0.625 Combine like terms: 10.019512214 + -0.625 = 9.394512214 x = 9.394512214 Simplifying x = 9.394512214Subproblem 2
x + 0.625 = -10.019512214 Simplifying x + 0.625 = -10.019512214 Reorder the terms: 0.625 + x = -10.019512214 Solving 0.625 + x = -10.019512214 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 = -10.019512214 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -10.019512214 + -0.625 x = -10.019512214 + -0.625 Combine like terms: -10.019512214 + -0.625 = -10.644512214 x = -10.644512214 Simplifying x = -10.644512214Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.394512214, -10.644512214}
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