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Simplifying x(4x + 5) = 360 Reorder the terms: x(5 + 4x) = 360 (5 * x + 4x * x) = 360 (5x + 4x2) = 360 Solving 5x + 4x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 5x + 4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -90 + 1.25x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 1.25x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 1.25x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 1.25x + x2 = 0 + 90 1.25x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 1.25x + x2 = 90 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 = 90 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 90 + 0.390625 Combine like terms: 90 + 0.390625 = 90.390625 0.390625 + 1.25x + x2 = 90.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 90.390625 Calculate the square root of the right side: 9.507398435 Break this problem into two subproblems by setting (x + 0.625) equal to 9.507398435 and -9.507398435.Subproblem 1
x + 0.625 = 9.507398435 Simplifying x + 0.625 = 9.507398435 Reorder the terms: 0.625 + x = 9.507398435 Solving 0.625 + x = 9.507398435 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 = 9.507398435 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 9.507398435 + -0.625 x = 9.507398435 + -0.625 Combine like terms: 9.507398435 + -0.625 = 8.882398435 x = 8.882398435 Simplifying x = 8.882398435Subproblem 2
x + 0.625 = -9.507398435 Simplifying x + 0.625 = -9.507398435 Reorder the terms: 0.625 + x = -9.507398435 Solving 0.625 + x = -9.507398435 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 = -9.507398435 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -9.507398435 + -0.625 x = -9.507398435 + -0.625 Combine like terms: -9.507398435 + -0.625 = -10.132398435 x = -10.132398435 Simplifying x = -10.132398435Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.882398435, -10.132398435}
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