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Simplifying 350 = (x + -8)(x + -8)(3.5) Reorder the terms: 350 = (-8 + x)(x + -8)(3.5) Reorder the terms: 350 = (-8 + x)(-8 + x)(3.5) Reorder the terms for easier multiplication: 350 = 3.5(-8 + x)(-8 + x) Multiply (-8 + x) * (-8 + x) 350 = 3.5(-8(-8 + x) + x(-8 + x)) 350 = 3.5((-8 * -8 + x * -8) + x(-8 + x)) 350 = 3.5((64 + -8x) + x(-8 + x)) 350 = 3.5(64 + -8x + (-8 * x + x * x)) 350 = 3.5(64 + -8x + (-8x + x2)) Combine like terms: -8x + -8x = -16x 350 = 3.5(64 + -16x + x2) 350 = (64 * 3.5 + -16x * 3.5 + x2 * 3.5) 350 = (224 + -56x + 3.5x2) Solving 350 = 224 + -56x + 3.5x2 Solving for variable 'x'. Combine like terms: 350 + -224 = 126 126 + 56x + -3.5x2 = 224 + -56x + 3.5x2 + -224 + 56x + -3.5x2 Reorder the terms: 126 + 56x + -3.5x2 = 224 + -224 + -56x + 56x + 3.5x2 + -3.5x2 Combine like terms: 224 + -224 = 0 126 + 56x + -3.5x2 = 0 + -56x + 56x + 3.5x2 + -3.5x2 126 + 56x + -3.5x2 = -56x + 56x + 3.5x2 + -3.5x2 Combine like terms: -56x + 56x = 0 126 + 56x + -3.5x2 = 0 + 3.5x2 + -3.5x2 126 + 56x + -3.5x2 = 3.5x2 + -3.5x2 Combine like terms: 3.5x2 + -3.5x2 = 0.0 126 + 56x + -3.5x2 = 0.0 Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. -36 + -16x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -16x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -16x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -16x + x2 = 0 + 36 -16x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -16x + x2 = 36 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 36 + 64 Reorder the terms: 64 + -16x + x2 = 36 + 64 Combine like terms: 36 + 64 = 100 64 + -16x + x2 = 100 Factor a perfect square on the left side: (x + -8)(x + -8) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -8) equal to 10 and -10.Subproblem 1
x + -8 = 10 Simplifying x + -8 = 10 Reorder the terms: -8 + x = 10 Solving -8 + x = 10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 10 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10 + 8 x = 10 + 8 Combine like terms: 10 + 8 = 18 x = 18 Simplifying x = 18Subproblem 2
x + -8 = -10 Simplifying x + -8 = -10 Reorder the terms: -8 + x = -10 Solving -8 + x = -10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -10 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10 + 8 x = -10 + 8 Combine like terms: -10 + 8 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {18, -2}
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