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Simplifying (3x + -14)(2x + 9) = 90 Reorder the terms: (-14 + 3x)(2x + 9) = 90 Reorder the terms: (-14 + 3x)(9 + 2x) = 90 Multiply (-14 + 3x) * (9 + 2x) (-14(9 + 2x) + 3x * (9 + 2x)) = 90 ((9 * -14 + 2x * -14) + 3x * (9 + 2x)) = 90 ((-126 + -28x) + 3x * (9 + 2x)) = 90 (-126 + -28x + (9 * 3x + 2x * 3x)) = 90 (-126 + -28x + (27x + 6x2)) = 90 Combine like terms: -28x + 27x = -1x (-126 + -1x + 6x2) = 90 Solving -126 + -1x + 6x2 = 90 Solving for variable 'x'. Reorder the terms: -126 + -90 + -1x + 6x2 = 90 + -90 Combine like terms: -126 + -90 = -216 -216 + -1x + 6x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -216 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -36 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -0.1666666667x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -0.1666666667x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -0.1666666667x + x2 = 0 + 36 -0.1666666667x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -0.1666666667x + x2 = 36 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 36 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 36 + 0.006944444447 Combine like terms: 36 + 0.006944444447 = 36.006944444447 0.006944444447 + -0.1666666667x + x2 = 36.006944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 36.006944444447 Calculate the square root of the right side: 6.000578676 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 6.000578676 and -6.000578676.Subproblem 1
x + -0.08333333335 = 6.000578676 Simplifying x + -0.08333333335 = 6.000578676 Reorder the terms: -0.08333333335 + x = 6.000578676 Solving -0.08333333335 + x = 6.000578676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 6.000578676 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 6.000578676 + 0.08333333335 x = 6.000578676 + 0.08333333335 Combine like terms: 6.000578676 + 0.08333333335 = 6.08391200935 x = 6.08391200935 Simplifying x = 6.08391200935Subproblem 2
x + -0.08333333335 = -6.000578676 Simplifying x + -0.08333333335 = -6.000578676 Reorder the terms: -0.08333333335 + x = -6.000578676 Solving -0.08333333335 + x = -6.000578676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -6.000578676 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -6.000578676 + 0.08333333335 x = -6.000578676 + 0.08333333335 Combine like terms: -6.000578676 + 0.08333333335 = -5.91724534265 x = -5.91724534265 Simplifying x = -5.91724534265Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.08391200935, -5.91724534265}
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