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Simplifying 168x + 1.75x2 = 0.5 Solving 168x + 1.75x2 = 0.5 Solving for variable 'x'. Reorder the terms: -0.5 + 168x + 1.75x2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + 168x + 1.75x2 = 0.0 Begin completing the square. Divide all terms by 1.75 the coefficient of the squared term: Divide each side by '1.75'. -0.2857142857 + 96x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 96x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 96x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 96x + x2 = 0 + 0.2857142857 96x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 96x + x2 = 0.2857142857 The x term is 96x. Take half its coefficient (48). Square it (2304) and add it to both sides. Add '2304' to each side of the equation. 96x + 2304 + x2 = 0.2857142857 + 2304 Reorder the terms: 2304 + 96x + x2 = 0.2857142857 + 2304 Combine like terms: 0.2857142857 + 2304 = 2304.2857142857 2304 + 96x + x2 = 2304.2857142857 Factor a perfect square on the left side: (x + 48)(x + 48) = 2304.2857142857 Calculate the square root of the right side: 48.002976098 Break this problem into two subproblems by setting (x + 48) equal to 48.002976098 and -48.002976098.Subproblem 1
x + 48 = 48.002976098 Simplifying x + 48 = 48.002976098 Reorder the terms: 48 + x = 48.002976098 Solving 48 + x = 48.002976098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + x = 48.002976098 + -48 Combine like terms: 48 + -48 = 0 0 + x = 48.002976098 + -48 x = 48.002976098 + -48 Combine like terms: 48.002976098 + -48 = 0.002976098 x = 0.002976098 Simplifying x = 0.002976098Subproblem 2
x + 48 = -48.002976098 Simplifying x + 48 = -48.002976098 Reorder the terms: 48 + x = -48.002976098 Solving 48 + x = -48.002976098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + x = -48.002976098 + -48 Combine like terms: 48 + -48 = 0 0 + x = -48.002976098 + -48 x = -48.002976098 + -48 Combine like terms: -48.002976098 + -48 = -96.002976098 x = -96.002976098 Simplifying x = -96.002976098Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.002976098, -96.002976098}
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