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Simplifying -4x2 + 5x + 22 = 0 Reorder the terms: 22 + 5x + -4x2 = 0 Solving 22 + 5x + -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'. -5.5 + -1.25x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -1.25x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -1.25x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -1.25x + x2 = 0 + 5.5 -1.25x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -1.25x + x2 = 5.5 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 5.5 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 5.5 + 0.390625 Combine like terms: 5.5 + 0.390625 = 5.890625 0.390625 + -1.25x + x2 = 5.890625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + -0.625) equal to 2.42706098 and -2.42706098.Subproblem 1
x + -0.625 = 2.42706098 Simplifying x + -0.625 = 2.42706098 Reorder the terms: -0.625 + x = 2.42706098 Solving -0.625 + x = 2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 2.42706098 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.42706098 + 0.625 x = 2.42706098 + 0.625 Combine like terms: 2.42706098 + 0.625 = 3.05206098 x = 3.05206098 Simplifying x = 3.05206098Subproblem 2
x + -0.625 = -2.42706098 Simplifying x + -0.625 = -2.42706098 Reorder the terms: -0.625 + x = -2.42706098 Solving -0.625 + x = -2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -2.42706098 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.42706098 + 0.625 x = -2.42706098 + 0.625 Combine like terms: -2.42706098 + 0.625 = -1.80206098 x = -1.80206098 Simplifying x = -1.80206098Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.05206098, -1.80206098}
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