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Simplifying -4x2 + 7x + 41 = 0 Reorder the terms: 41 + 7x + -4x2 = 0 Solving 41 + 7x + -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'. -10.25 + -1.75x + x2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + -1.75x + 10.25 + x2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + -1.75x + x2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + -1.75x + x2 = 0 + 10.25 -1.75x + x2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 -1.75x + x2 = 10.25 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 10.25 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 10.25 + 0.765625 Combine like terms: 10.25 + 0.765625 = 11.015625 0.765625 + -1.75x + x2 = 11.015625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 11.015625 Calculate the square root of the right side: 3.318979512 Break this problem into two subproblems by setting (x + -0.875) equal to 3.318979512 and -3.318979512.Subproblem 1
x + -0.875 = 3.318979512 Simplifying x + -0.875 = 3.318979512 Reorder the terms: -0.875 + x = 3.318979512 Solving -0.875 + x = 3.318979512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 3.318979512 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 3.318979512 + 0.875 x = 3.318979512 + 0.875 Combine like terms: 3.318979512 + 0.875 = 4.193979512 x = 4.193979512 Simplifying x = 4.193979512Subproblem 2
x + -0.875 = -3.318979512 Simplifying x + -0.875 = -3.318979512 Reorder the terms: -0.875 + x = -3.318979512 Solving -0.875 + x = -3.318979512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -3.318979512 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -3.318979512 + 0.875 x = -3.318979512 + 0.875 Combine like terms: -3.318979512 + 0.875 = -2.443979512 x = -2.443979512 Simplifying x = -2.443979512Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.193979512, -2.443979512}
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