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Simplifying 4x2 + -1x = 43 Reorder the terms: -1x + 4x2 = 43 Solving -1x + 4x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + -1x + 4x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.75 + -0.25x + x2 = 0 Move the constant term to the right: Add '10.75' to each side of the equation. -10.75 + -0.25x + 10.75 + x2 = 0 + 10.75 Reorder the terms: -10.75 + 10.75 + -0.25x + x2 = 0 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + -0.25x + x2 = 0 + 10.75 -0.25x + x2 = 0 + 10.75 Combine like terms: 0 + 10.75 = 10.75 -0.25x + x2 = 10.75 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 10.75 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 10.75 + 0.015625 Combine like terms: 10.75 + 0.015625 = 10.765625 0.015625 + -0.25x + x2 = 10.765625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 10.765625 Calculate the square root of the right side: 3.281101187 Break this problem into two subproblems by setting (x + -0.125) equal to 3.281101187 and -3.281101187.Subproblem 1
x + -0.125 = 3.281101187 Simplifying x + -0.125 = 3.281101187 Reorder the terms: -0.125 + x = 3.281101187 Solving -0.125 + x = 3.281101187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 3.281101187 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 3.281101187 + 0.125 x = 3.281101187 + 0.125 Combine like terms: 3.281101187 + 0.125 = 3.406101187 x = 3.406101187 Simplifying x = 3.406101187Subproblem 2
x + -0.125 = -3.281101187 Simplifying x + -0.125 = -3.281101187 Reorder the terms: -0.125 + x = -3.281101187 Solving -0.125 + x = -3.281101187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -3.281101187 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -3.281101187 + 0.125 x = -3.281101187 + 0.125 Combine like terms: -3.281101187 + 0.125 = -3.156101187 x = -3.156101187 Simplifying x = -3.156101187Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.406101187, -3.156101187}
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