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Simplifying (4x + 9) * x + -49 = 501 Reorder the terms: (9 + 4x) * x + -49 = 501 Reorder the terms for easier multiplication: x(9 + 4x) + -49 = 501 (9 * x + 4x * x) + -49 = 501 (9x + 4x2) + -49 = 501 Reorder the terms: -49 + 9x + 4x2 = 501 Solving -49 + 9x + 4x2 = 501 Solving for variable 'x'. Reorder the terms: -49 + -501 + 9x + 4x2 = 501 + -501 Combine like terms: -49 + -501 = -550 -550 + 9x + 4x2 = 501 + -501 Combine like terms: 501 + -501 = 0 -550 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -137.5 + 2.25x + x2 = 0 Move the constant term to the right: Add '137.5' to each side of the equation. -137.5 + 2.25x + 137.5 + x2 = 0 + 137.5 Reorder the terms: -137.5 + 137.5 + 2.25x + x2 = 0 + 137.5 Combine like terms: -137.5 + 137.5 = 0.0 0.0 + 2.25x + x2 = 0 + 137.5 2.25x + x2 = 0 + 137.5 Combine like terms: 0 + 137.5 = 137.5 2.25x + x2 = 137.5 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 137.5 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 137.5 + 1.265625 Combine like terms: 137.5 + 1.265625 = 138.765625 1.265625 + 2.25x + x2 = 138.765625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 138.765625 Calculate the square root of the right side: 11.779882215 Break this problem into two subproblems by setting (x + 1.125) equal to 11.779882215 and -11.779882215.Subproblem 1
x + 1.125 = 11.779882215 Simplifying x + 1.125 = 11.779882215 Reorder the terms: 1.125 + x = 11.779882215 Solving 1.125 + x = 11.779882215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 11.779882215 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 11.779882215 + -1.125 x = 11.779882215 + -1.125 Combine like terms: 11.779882215 + -1.125 = 10.654882215 x = 10.654882215 Simplifying x = 10.654882215Subproblem 2
x + 1.125 = -11.779882215 Simplifying x + 1.125 = -11.779882215 Reorder the terms: 1.125 + x = -11.779882215 Solving 1.125 + x = -11.779882215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -11.779882215 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -11.779882215 + -1.125 x = -11.779882215 + -1.125 Combine like terms: -11.779882215 + -1.125 = -12.904882215 x = -12.904882215 Simplifying x = -12.904882215Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.654882215, -12.904882215}
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