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Simplifying (4x + 5)(x) = 280 Reorder the terms: (5 + 4x)(x) = 280 Reorder the terms for easier multiplication: x(5 + 4x) = 280 (5 * x + 4x * x) = 280 (5x + 4x2) = 280 Solving 5x + 4x2 = 280 Solving for variable 'x'. Reorder the terms: -280 + 5x + 4x2 = 280 + -280 Combine like terms: 280 + -280 = 0 -280 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -70 + 1.25x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 1.25x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 1.25x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 1.25x + x2 = 0 + 70 1.25x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 1.25x + x2 = 70 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 = 70 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 70 + 0.390625 Combine like terms: 70 + 0.390625 = 70.390625 0.390625 + 1.25x + x2 = 70.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 70.390625 Calculate the square root of the right side: 8.389912097 Break this problem into two subproblems by setting (x + 0.625) equal to 8.389912097 and -8.389912097.Subproblem 1
x + 0.625 = 8.389912097 Simplifying x + 0.625 = 8.389912097 Reorder the terms: 0.625 + x = 8.389912097 Solving 0.625 + x = 8.389912097 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 = 8.389912097 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 8.389912097 + -0.625 x = 8.389912097 + -0.625 Combine like terms: 8.389912097 + -0.625 = 7.764912097 x = 7.764912097 Simplifying x = 7.764912097Subproblem 2
x + 0.625 = -8.389912097 Simplifying x + 0.625 = -8.389912097 Reorder the terms: 0.625 + x = -8.389912097 Solving 0.625 + x = -8.389912097 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 = -8.389912097 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -8.389912097 + -0.625 x = -8.389912097 + -0.625 Combine like terms: -8.389912097 + -0.625 = -9.014912097 x = -9.014912097 Simplifying x = -9.014912097Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.764912097, -9.014912097}
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