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Simplifying (x + -15)(2x + -165) + 90 = 0 Reorder the terms: (-15 + x)(2x + -165) + 90 = 0 Reorder the terms: (-15 + x)(-165 + 2x) + 90 = 0 Multiply (-15 + x) * (-165 + 2x) (-15(-165 + 2x) + x(-165 + 2x)) + 90 = 0 ((-165 * -15 + 2x * -15) + x(-165 + 2x)) + 90 = 0 ((2475 + -30x) + x(-165 + 2x)) + 90 = 0 (2475 + -30x + (-165 * x + 2x * x)) + 90 = 0 (2475 + -30x + (-165x + 2x2)) + 90 = 0 Combine like terms: -30x + -165x = -195x (2475 + -195x + 2x2) + 90 = 0 Reorder the terms: 2475 + 90 + -195x + 2x2 = 0 Combine like terms: 2475 + 90 = 2565 2565 + -195x + 2x2 = 0 Solving 2565 + -195x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1282.5 + -97.5x + x2 = 0 Move the constant term to the right: Add '-1282.5' to each side of the equation. 1282.5 + -97.5x + -1282.5 + x2 = 0 + -1282.5 Reorder the terms: 1282.5 + -1282.5 + -97.5x + x2 = 0 + -1282.5 Combine like terms: 1282.5 + -1282.5 = 0.0 0.0 + -97.5x + x2 = 0 + -1282.5 -97.5x + x2 = 0 + -1282.5 Combine like terms: 0 + -1282.5 = -1282.5 -97.5x + x2 = -1282.5 The x term is -97.5x. Take half its coefficient (-48.75). Square it (2376.5625) and add it to both sides. Add '2376.5625' to each side of the equation. -97.5x + 2376.5625 + x2 = -1282.5 + 2376.5625 Reorder the terms: 2376.5625 + -97.5x + x2 = -1282.5 + 2376.5625 Combine like terms: -1282.5 + 2376.5625 = 1094.0625 2376.5625 + -97.5x + x2 = 1094.0625 Factor a perfect square on the left side: (x + -48.75)(x + -48.75) = 1094.0625 Calculate the square root of the right side: 33.076615607 Break this problem into two subproblems by setting (x + -48.75) equal to 33.076615607 and -33.076615607.Subproblem 1
x + -48.75 = 33.076615607 Simplifying x + -48.75 = 33.076615607 Reorder the terms: -48.75 + x = 33.076615607 Solving -48.75 + x = 33.076615607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48.75' to each side of the equation. -48.75 + 48.75 + x = 33.076615607 + 48.75 Combine like terms: -48.75 + 48.75 = 0.00 0.00 + x = 33.076615607 + 48.75 x = 33.076615607 + 48.75 Combine like terms: 33.076615607 + 48.75 = 81.826615607 x = 81.826615607 Simplifying x = 81.826615607Subproblem 2
x + -48.75 = -33.076615607 Simplifying x + -48.75 = -33.076615607 Reorder the terms: -48.75 + x = -33.076615607 Solving -48.75 + x = -33.076615607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48.75' to each side of the equation. -48.75 + 48.75 + x = -33.076615607 + 48.75 Combine like terms: -48.75 + 48.75 = 0.00 0.00 + x = -33.076615607 + 48.75 x = -33.076615607 + 48.75 Combine like terms: -33.076615607 + 48.75 = 15.673384393 x = 15.673384393 Simplifying x = 15.673384393Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.826615607, 15.673384393}
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