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Simplifying 4x2 + x + -85 = 180 Reorder the terms: -85 + x + 4x2 = 180 Solving -85 + x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -85 + -180 + x + 4x2 = 180 + -180 Combine like terms: -85 + -180 = -265 -265 + x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -265 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -66.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '66.25' to each side of the equation. -66.25 + 0.25x + 66.25 + x2 = 0 + 66.25 Reorder the terms: -66.25 + 66.25 + 0.25x + x2 = 0 + 66.25 Combine like terms: -66.25 + 66.25 = 0.00 0.00 + 0.25x + x2 = 0 + 66.25 0.25x + x2 = 0 + 66.25 Combine like terms: 0 + 66.25 = 66.25 0.25x + x2 = 66.25 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. 0.25x + 0.25 + x2 = 66.25 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 66.25 + 0.25 Combine like terms: 66.25 + 0.25 = 66.5 0.25 + 0.25x + x2 = 66.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 66.5 Calculate the square root of the right side: 8.154753215 Break this problem into two subproblems by setting (x + 0.5) equal to 8.154753215 and -8.154753215.Subproblem 1
x + 0.5 = 8.154753215 Simplifying x + 0.5 = 8.154753215 Reorder the terms: 0.5 + x = 8.154753215 Solving 0.5 + x = 8.154753215 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 = 8.154753215 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.154753215 + -0.5 x = 8.154753215 + -0.5 Combine like terms: 8.154753215 + -0.5 = 7.654753215 x = 7.654753215 Simplifying x = 7.654753215Subproblem 2
x + 0.5 = -8.154753215 Simplifying x + 0.5 = -8.154753215 Reorder the terms: 0.5 + x = -8.154753215 Solving 0.5 + x = -8.154753215 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 = -8.154753215 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.154753215 + -0.5 x = -8.154753215 + -0.5 Combine like terms: -8.154753215 + -0.5 = -8.654753215 x = -8.654753215 Simplifying x = -8.654753215Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.654753215, -8.654753215}
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