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Simplifying (2x + -5)(3x + 7) = 325 Reorder the terms: (-5 + 2x)(3x + 7) = 325 Reorder the terms: (-5 + 2x)(7 + 3x) = 325 Multiply (-5 + 2x) * (7 + 3x) (-5(7 + 3x) + 2x * (7 + 3x)) = 325 ((7 * -5 + 3x * -5) + 2x * (7 + 3x)) = 325 ((-35 + -15x) + 2x * (7 + 3x)) = 325 (-35 + -15x + (7 * 2x + 3x * 2x)) = 325 (-35 + -15x + (14x + 6x2)) = 325 Combine like terms: -15x + 14x = -1x (-35 + -1x + 6x2) = 325 Solving -35 + -1x + 6x2 = 325 Solving for variable 'x'. Reorder the terms: -35 + -325 + -1x + 6x2 = 325 + -325 Combine like terms: -35 + -325 = -360 -360 + -1x + 6x2 = 325 + -325 Combine like terms: 325 + -325 = 0 -360 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -60 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -0.1666666667x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -0.1666666667x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -0.1666666667x + x2 = 0 + 60 -0.1666666667x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -0.1666666667x + x2 = 60 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 = 60 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 60 + 0.006944444447 Combine like terms: 60 + 0.006944444447 = 60.006944444447 0.006944444447 + -0.1666666667x + x2 = 60.006944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 60.006944444447 Calculate the square root of the right side: 7.746414941 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 7.746414941 and -7.746414941.Subproblem 1
x + -0.08333333335 = 7.746414941 Simplifying x + -0.08333333335 = 7.746414941 Reorder the terms: -0.08333333335 + x = 7.746414941 Solving -0.08333333335 + x = 7.746414941 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 = 7.746414941 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 7.746414941 + 0.08333333335 x = 7.746414941 + 0.08333333335 Combine like terms: 7.746414941 + 0.08333333335 = 7.82974827435 x = 7.82974827435 Simplifying x = 7.82974827435Subproblem 2
x + -0.08333333335 = -7.746414941 Simplifying x + -0.08333333335 = -7.746414941 Reorder the terms: -0.08333333335 + x = -7.746414941 Solving -0.08333333335 + x = -7.746414941 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 = -7.746414941 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -7.746414941 + 0.08333333335 x = -7.746414941 + 0.08333333335 Combine like terms: -7.746414941 + 0.08333333335 = -7.66308160765 x = -7.66308160765 Simplifying x = -7.66308160765Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.82974827435, -7.66308160765}
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