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Simplifying (4x + 5)(x + -6) = 7 Reorder the terms: (5 + 4x)(x + -6) = 7 Reorder the terms: (5 + 4x)(-6 + x) = 7 Multiply (5 + 4x) * (-6 + x) (5(-6 + x) + 4x * (-6 + x)) = 7 ((-6 * 5 + x * 5) + 4x * (-6 + x)) = 7 ((-30 + 5x) + 4x * (-6 + x)) = 7 (-30 + 5x + (-6 * 4x + x * 4x)) = 7 (-30 + 5x + (-24x + 4x2)) = 7 Combine like terms: 5x + -24x = -19x (-30 + -19x + 4x2) = 7 Solving -30 + -19x + 4x2 = 7 Solving for variable 'x'. Reorder the terms: -30 + -7 + -19x + 4x2 = 7 + -7 Combine like terms: -30 + -7 = -37 -37 + -19x + 4x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -37 + -19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + -4.75x + x2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + -4.75x + 9.25 + x2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + -4.75x + x2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + -4.75x + x2 = 0 + 9.25 -4.75x + x2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 -4.75x + x2 = 9.25 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 9.25 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 9.25 + 5.640625 Combine like terms: 9.25 + 5.640625 = 14.890625 5.640625 + -4.75x + x2 = 14.890625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 14.890625 Calculate the square root of the right side: 3.85883726 Break this problem into two subproblems by setting (x + -2.375) equal to 3.85883726 and -3.85883726.Subproblem 1
x + -2.375 = 3.85883726 Simplifying x + -2.375 = 3.85883726 Reorder the terms: -2.375 + x = 3.85883726 Solving -2.375 + x = 3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 3.85883726 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 3.85883726 + 2.375 x = 3.85883726 + 2.375 Combine like terms: 3.85883726 + 2.375 = 6.23383726 x = 6.23383726 Simplifying x = 6.23383726Subproblem 2
x + -2.375 = -3.85883726 Simplifying x + -2.375 = -3.85883726 Reorder the terms: -2.375 + x = -3.85883726 Solving -2.375 + x = -3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -3.85883726 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -3.85883726 + 2.375 x = -3.85883726 + 2.375 Combine like terms: -3.85883726 + 2.375 = -1.48383726 x = -1.48383726 Simplifying x = -1.48383726Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.23383726, -1.48383726}
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