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Simplifying 4x2 + -43x + 7 = 0 Reorder the terms: 7 + -43x + 4x2 = 0 Solving 7 + -43x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -10.75x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -10.75x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -10.75x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -10.75x + x2 = 0 + -1.75 -10.75x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -10.75x + x2 = -1.75 The x term is -10.75x. Take half its coefficient (-5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. -10.75x + 28.890625 + x2 = -1.75 + 28.890625 Reorder the terms: 28.890625 + -10.75x + x2 = -1.75 + 28.890625 Combine like terms: -1.75 + 28.890625 = 27.140625 28.890625 + -10.75x + x2 = 27.140625 Factor a perfect square on the left side: (x + -5.375)(x + -5.375) = 27.140625 Calculate the square root of the right side: 5.209666496 Break this problem into two subproblems by setting (x + -5.375) equal to 5.209666496 and -5.209666496.Subproblem 1
x + -5.375 = 5.209666496 Simplifying x + -5.375 = 5.209666496 Reorder the terms: -5.375 + x = 5.209666496 Solving -5.375 + x = 5.209666496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.375' to each side of the equation. -5.375 + 5.375 + x = 5.209666496 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = 5.209666496 + 5.375 x = 5.209666496 + 5.375 Combine like terms: 5.209666496 + 5.375 = 10.584666496 x = 10.584666496 Simplifying x = 10.584666496Subproblem 2
x + -5.375 = -5.209666496 Simplifying x + -5.375 = -5.209666496 Reorder the terms: -5.375 + x = -5.209666496 Solving -5.375 + x = -5.209666496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.375' to each side of the equation. -5.375 + 5.375 + x = -5.209666496 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = -5.209666496 + 5.375 x = -5.209666496 + 5.375 Combine like terms: -5.209666496 + 5.375 = 0.165333504 x = 0.165333504 Simplifying x = 0.165333504Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.584666496, 0.165333504}
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