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Simplifying 4x2 + 38x + -21 = 0 Reorder the terms: -21 + 38x + 4x2 = 0 Solving -21 + 38x + 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'. -5.25 + 9.5x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 9.5x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 9.5x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 9.5x + x2 = 0 + 5.25 9.5x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 9.5x + x2 = 5.25 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 5.25 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 5.25 + 22.5625 Combine like terms: 5.25 + 22.5625 = 27.8125 22.5625 + 9.5x + x2 = 27.8125 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 27.8125 Calculate the square root of the right side: 5.273755777 Break this problem into two subproblems by setting (x + 4.75) equal to 5.273755777 and -5.273755777.Subproblem 1
x + 4.75 = 5.273755777 Simplifying x + 4.75 = 5.273755777 Reorder the terms: 4.75 + x = 5.273755777 Solving 4.75 + x = 5.273755777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 5.273755777 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 5.273755777 + -4.75 x = 5.273755777 + -4.75 Combine like terms: 5.273755777 + -4.75 = 0.523755777 x = 0.523755777 Simplifying x = 0.523755777Subproblem 2
x + 4.75 = -5.273755777 Simplifying x + 4.75 = -5.273755777 Reorder the terms: 4.75 + x = -5.273755777 Solving 4.75 + x = -5.273755777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -5.273755777 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -5.273755777 + -4.75 x = -5.273755777 + -4.75 Combine like terms: -5.273755777 + -4.75 = -10.023755777 x = -10.023755777 Simplifying x = -10.023755777Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.523755777, -10.023755777}
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