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Simplifying -1x(13 + -4x) = -3(5 + -9x) + 2 (13 * -1x + -4x * -1x) = -3(5 + -9x) + 2 (-13x + 4x2) = -3(5 + -9x) + 2 -13x + 4x2 = (5 * -3 + -9x * -3) + 2 -13x + 4x2 = (-15 + 27x) + 2 Reorder the terms: -13x + 4x2 = -15 + 2 + 27x Combine like terms: -15 + 2 = -13 -13x + 4x2 = -13 + 27x Solving -13x + 4x2 = -13 + 27x Solving for variable 'x'. Reorder the terms: 13 + -13x + -27x + 4x2 = -13 + 27x + 13 + -27x Combine like terms: -13x + -27x = -40x 13 + -40x + 4x2 = -13 + 27x + 13 + -27x Reorder the terms: 13 + -40x + 4x2 = -13 + 13 + 27x + -27x Combine like terms: -13 + 13 = 0 13 + -40x + 4x2 = 0 + 27x + -27x 13 + -40x + 4x2 = 27x + -27x Combine like terms: 27x + -27x = 0 13 + -40x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + -10x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -10x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -10x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -10x + x2 = 0 + -3.25 -10x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -10x + x2 = -3.25 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -3.25 + 25 Reorder the terms: 25 + -10x + x2 = -3.25 + 25 Combine like terms: -3.25 + 25 = 21.75 25 + -10x + x2 = 21.75 Factor a perfect square on the left side: (x + -5)(x + -5) = 21.75 Calculate the square root of the right side: 4.663689527 Break this problem into two subproblems by setting (x + -5) equal to 4.663689527 and -4.663689527.Subproblem 1
x + -5 = 4.663689527 Simplifying x + -5 = 4.663689527 Reorder the terms: -5 + x = 4.663689527 Solving -5 + x = 4.663689527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.663689527 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.663689527 + 5 x = 4.663689527 + 5 Combine like terms: 4.663689527 + 5 = 9.663689527 x = 9.663689527 Simplifying x = 9.663689527Subproblem 2
x + -5 = -4.663689527 Simplifying x + -5 = -4.663689527 Reorder the terms: -5 + x = -4.663689527 Solving -5 + x = -4.663689527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.663689527 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.663689527 + 5 x = -4.663689527 + 5 Combine like terms: -4.663689527 + 5 = 0.336310473 x = 0.336310473 Simplifying x = 0.336310473Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.663689527, 0.336310473}
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