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Simplifying 9x + -4x(x + 8) = 3(2x + -7) Reorder the terms: 9x + -4x(8 + x) = 3(2x + -7) 9x + (8 * -4x + x * -4x) = 3(2x + -7) 9x + (-32x + -4x2) = 3(2x + -7) Combine like terms: 9x + -32x = -23x -23x + -4x2 = 3(2x + -7) Reorder the terms: -23x + -4x2 = 3(-7 + 2x) -23x + -4x2 = (-7 * 3 + 2x * 3) -23x + -4x2 = (-21 + 6x) Solving -23x + -4x2 = -21 + 6x Solving for variable 'x'. Reorder the terms: 21 + -23x + -6x + -4x2 = -21 + 6x + 21 + -6x Combine like terms: -23x + -6x = -29x 21 + -29x + -4x2 = -21 + 6x + 21 + -6x Reorder the terms: 21 + -29x + -4x2 = -21 + 21 + 6x + -6x Combine like terms: -21 + 21 = 0 21 + -29x + -4x2 = 0 + 6x + -6x 21 + -29x + -4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 21 + -29x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.25 + 7.25x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 7.25x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 7.25x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 7.25x + x2 = 0 + 5.25 7.25x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 7.25x + x2 = 5.25 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = 5.25 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = 5.25 + 13.140625 Combine like terms: 5.25 + 13.140625 = 18.390625 13.140625 + 7.25x + x2 = 18.390625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 18.390625 Calculate the square root of the right side: 4.2884292 Break this problem into two subproblems by setting (x + 3.625) equal to 4.2884292 and -4.2884292.Subproblem 1
x + 3.625 = 4.2884292 Simplifying x + 3.625 = 4.2884292 Reorder the terms: 3.625 + x = 4.2884292 Solving 3.625 + x = 4.2884292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 4.2884292 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 4.2884292 + -3.625 x = 4.2884292 + -3.625 Combine like terms: 4.2884292 + -3.625 = 0.6634292 x = 0.6634292 Simplifying x = 0.6634292Subproblem 2
x + 3.625 = -4.2884292 Simplifying x + 3.625 = -4.2884292 Reorder the terms: 3.625 + x = -4.2884292 Solving 3.625 + x = -4.2884292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -4.2884292 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -4.2884292 + -3.625 x = -4.2884292 + -3.625 Combine like terms: -4.2884292 + -3.625 = -7.9134292 x = -7.9134292 Simplifying x = -7.9134292Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6634292, -7.9134292}
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