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Simplifying 64x2 + x = 22 Reorder the terms: x + 64x2 = 22 Solving x + 64x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + x + 64x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.34375 + 0.015625x + x2 = 0 Move the constant term to the right: Add '0.34375' to each side of the equation. -0.34375 + 0.015625x + 0.34375 + x2 = 0 + 0.34375 Reorder the terms: -0.34375 + 0.34375 + 0.015625x + x2 = 0 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + 0.015625x + x2 = 0 + 0.34375 0.015625x + x2 = 0 + 0.34375 Combine like terms: 0 + 0.34375 = 0.34375 0.015625x + x2 = 0.34375 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.015625x + 0.25 + x2 = 0.34375 + 0.25 Reorder the terms: 0.25 + 0.015625x + x2 = 0.34375 + 0.25 Combine like terms: 0.34375 + 0.25 = 0.59375 0.25 + 0.015625x + x2 = 0.59375 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.59375 Calculate the square root of the right side: 0.77055175 Break this problem into two subproblems by setting (x + 0.5) equal to 0.77055175 and -0.77055175.Subproblem 1
x + 0.5 = 0.77055175 Simplifying x + 0.5 = 0.77055175 Reorder the terms: 0.5 + x = 0.77055175 Solving 0.5 + x = 0.77055175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.77055175 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.77055175 + -0.5 x = 0.77055175 + -0.5 Combine like terms: 0.77055175 + -0.5 = 0.27055175 x = 0.27055175 Simplifying x = 0.27055175Subproblem 2
x + 0.5 = -0.77055175 Simplifying x + 0.5 = -0.77055175 Reorder the terms: 0.5 + x = -0.77055175 Solving 0.5 + x = -0.77055175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.77055175 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.77055175 + -0.5 x = -0.77055175 + -0.5 Combine like terms: -0.77055175 + -0.5 = -1.27055175 x = -1.27055175 Simplifying x = -1.27055175Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.27055175, -1.27055175}
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