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Simplifying 306 = (x + -4)(x + -4)(8.5) Reorder the terms: 306 = (-4 + x)(x + -4)(8.5) Reorder the terms: 306 = (-4 + x)(-4 + x)(8.5) Reorder the terms for easier multiplication: 306 = 8.5(-4 + x)(-4 + x) Multiply (-4 + x) * (-4 + x) 306 = 8.5(-4(-4 + x) + x(-4 + x)) 306 = 8.5((-4 * -4 + x * -4) + x(-4 + x)) 306 = 8.5((16 + -4x) + x(-4 + x)) 306 = 8.5(16 + -4x + (-4 * x + x * x)) 306 = 8.5(16 + -4x + (-4x + x2)) Combine like terms: -4x + -4x = -8x 306 = 8.5(16 + -8x + x2) 306 = (16 * 8.5 + -8x * 8.5 + x2 * 8.5) 306 = (136 + -68x + 8.5x2) Solving 306 = 136 + -68x + 8.5x2 Solving for variable 'x'. Combine like terms: 306 + -136 = 170 170 + 68x + -8.5x2 = 136 + -68x + 8.5x2 + -136 + 68x + -8.5x2 Reorder the terms: 170 + 68x + -8.5x2 = 136 + -136 + -68x + 68x + 8.5x2 + -8.5x2 Combine like terms: 136 + -136 = 0 170 + 68x + -8.5x2 = 0 + -68x + 68x + 8.5x2 + -8.5x2 170 + 68x + -8.5x2 = -68x + 68x + 8.5x2 + -8.5x2 Combine like terms: -68x + 68x = 0 170 + 68x + -8.5x2 = 0 + 8.5x2 + -8.5x2 170 + 68x + -8.5x2 = 8.5x2 + -8.5x2 Combine like terms: 8.5x2 + -8.5x2 = 0.0 170 + 68x + -8.5x2 = 0.0 Begin completing the square. Divide all terms by -8.5 the coefficient of the squared term: Divide each side by '-8.5'. -20 + -8x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -8x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -8x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -8x + x2 = 0 + 20 -8x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -8x + x2 = 20 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 20 + 16 Reorder the terms: 16 + -8x + x2 = 20 + 16 Combine like terms: 20 + 16 = 36 16 + -8x + x2 = 36 Factor a perfect square on the left side: (x + -4)(x + -4) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -4) equal to 6 and -6.Subproblem 1
x + -4 = 6 Simplifying x + -4 = 6 Reorder the terms: -4 + x = 6 Solving -4 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6 + 4 x = 6 + 4 Combine like terms: 6 + 4 = 10 x = 10 Simplifying x = 10Subproblem 2
x + -4 = -6 Simplifying x + -4 = -6 Reorder the terms: -4 + x = -6 Solving -4 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6 + 4 x = -6 + 4 Combine like terms: -6 + 4 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -2}
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