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Simplifying 4x2 = x + 28 Reorder the terms: 4x2 = 28 + x Solving 4x2 = 28 + x Solving for variable 'x'. Reorder the terms: -28 + -1x + 4x2 = 28 + x + -28 + -1x Reorder the terms: -28 + -1x + 4x2 = 28 + -28 + x + -1x Combine like terms: 28 + -28 = 0 -28 + -1x + 4x2 = 0 + x + -1x -28 + -1x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -28 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7 + -0.25x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.25x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.25x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.25x + x2 = 0 + 7 -0.25x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.25x + x2 = 7 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 = 7 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 7 + 0.015625 Combine like terms: 7 + 0.015625 = 7.015625 0.015625 + -0.25x + x2 = 7.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 7.015625 Calculate the square root of the right side: 2.648702513 Break this problem into two subproblems by setting (x + -0.125) equal to 2.648702513 and -2.648702513.Subproblem 1
x + -0.125 = 2.648702513 Simplifying x + -0.125 = 2.648702513 Reorder the terms: -0.125 + x = 2.648702513 Solving -0.125 + x = 2.648702513 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 = 2.648702513 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.648702513 + 0.125 x = 2.648702513 + 0.125 Combine like terms: 2.648702513 + 0.125 = 2.773702513 x = 2.773702513 Simplifying x = 2.773702513Subproblem 2
x + -0.125 = -2.648702513 Simplifying x + -0.125 = -2.648702513 Reorder the terms: -0.125 + x = -2.648702513 Solving -0.125 + x = -2.648702513 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 = -2.648702513 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.648702513 + 0.125 x = -2.648702513 + 0.125 Combine like terms: -2.648702513 + 0.125 = -2.523702513 x = -2.523702513 Simplifying x = -2.523702513Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.773702513, -2.523702513}
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