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Simplifying 240 = (4x + 5)(x) Reorder the terms: 240 = (5 + 4x)(x) Reorder the terms for easier multiplication: 240 = x(5 + 4x) 240 = (5 * x + 4x * x) 240 = (5x + 4x2) Solving 240 = 5x + 4x2 Solving for variable 'x'. Reorder the terms: 240 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 240 + -5x + -4x2 = 0 + 4x2 + -4x2 240 + -5x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 240 + -5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -60 + 1.25x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 1.25x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 1.25x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 1.25x + x2 = 0 + 60 1.25x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 1.25x + x2 = 60 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 = 60 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 60 + 0.390625 Combine like terms: 60 + 0.390625 = 60.390625 0.390625 + 1.25x + x2 = 60.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 60.390625 Calculate the square root of the right side: 7.771140521 Break this problem into two subproblems by setting (x + 0.625) equal to 7.771140521 and -7.771140521.Subproblem 1
x + 0.625 = 7.771140521 Simplifying x + 0.625 = 7.771140521 Reorder the terms: 0.625 + x = 7.771140521 Solving 0.625 + x = 7.771140521 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 = 7.771140521 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 7.771140521 + -0.625 x = 7.771140521 + -0.625 Combine like terms: 7.771140521 + -0.625 = 7.146140521 x = 7.146140521 Simplifying x = 7.146140521Subproblem 2
x + 0.625 = -7.771140521 Simplifying x + 0.625 = -7.771140521 Reorder the terms: 0.625 + x = -7.771140521 Solving 0.625 + x = -7.771140521 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 = -7.771140521 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -7.771140521 + -0.625 x = -7.771140521 + -0.625 Combine like terms: -7.771140521 + -0.625 = -8.396140521 x = -8.396140521 Simplifying x = -8.396140521Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.146140521, -8.396140521}
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