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Simplifying 4x2 + -1x + -84 = 0 Reorder the terms: -84 + -1x + 4x2 = 0 Solving -84 + -1x + 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 + -0.25x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -0.25x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -0.25x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -0.25x + x2 = 0 + 21 -0.25x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -0.25x + x2 = 21 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 = 21 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 21 + 0.015625 Combine like terms: 21 + 0.015625 = 21.015625 0.015625 + -0.25x + x2 = 21.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 21.015625 Calculate the square root of the right side: 4.584280205 Break this problem into two subproblems by setting (x + -0.125) equal to 4.584280205 and -4.584280205.Subproblem 1
x + -0.125 = 4.584280205 Simplifying x + -0.125 = 4.584280205 Reorder the terms: -0.125 + x = 4.584280205 Solving -0.125 + x = 4.584280205 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 = 4.584280205 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 4.584280205 + 0.125 x = 4.584280205 + 0.125 Combine like terms: 4.584280205 + 0.125 = 4.709280205 x = 4.709280205 Simplifying x = 4.709280205Subproblem 2
x + -0.125 = -4.584280205 Simplifying x + -0.125 = -4.584280205 Reorder the terms: -0.125 + x = -4.584280205 Solving -0.125 + x = -4.584280205 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 = -4.584280205 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -4.584280205 + 0.125 x = -4.584280205 + 0.125 Combine like terms: -4.584280205 + 0.125 = -4.459280205 x = -4.459280205 Simplifying x = -4.459280205Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.709280205, -4.459280205}
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