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Simplifying 4x2 + 7x + -86 = 0 Reorder the terms: -86 + 7x + 4x2 = 0 Solving -86 + 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'. -21.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '21.5' to each side of the equation. -21.5 + 1.75x + 21.5 + x2 = 0 + 21.5 Reorder the terms: -21.5 + 21.5 + 1.75x + x2 = 0 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + 1.75x + x2 = 0 + 21.5 1.75x + x2 = 0 + 21.5 Combine like terms: 0 + 21.5 = 21.5 1.75x + x2 = 21.5 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 = 21.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 21.5 + 0.765625 Combine like terms: 21.5 + 0.765625 = 22.265625 0.765625 + 1.75x + x2 = 22.265625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 22.265625 Calculate the square root of the right side: 4.718646522 Break this problem into two subproblems by setting (x + 0.875) equal to 4.718646522 and -4.718646522.Subproblem 1
x + 0.875 = 4.718646522 Simplifying x + 0.875 = 4.718646522 Reorder the terms: 0.875 + x = 4.718646522 Solving 0.875 + x = 4.718646522 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 = 4.718646522 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 4.718646522 + -0.875 x = 4.718646522 + -0.875 Combine like terms: 4.718646522 + -0.875 = 3.843646522 x = 3.843646522 Simplifying x = 3.843646522Subproblem 2
x + 0.875 = -4.718646522 Simplifying x + 0.875 = -4.718646522 Reorder the terms: 0.875 + x = -4.718646522 Solving 0.875 + x = -4.718646522 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 = -4.718646522 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -4.718646522 + -0.875 x = -4.718646522 + -0.875 Combine like terms: -4.718646522 + -0.875 = -5.593646522 x = -5.593646522 Simplifying x = -5.593646522Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.843646522, -5.593646522}
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