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Simplifying 4x2 + 8x + -72 = -3 Reorder the terms: -72 + 8x + 4x2 = -3 Solving -72 + 8x + 4x2 = -3 Solving for variable 'x'. Reorder the terms: -72 + 3 + 8x + 4x2 = -3 + 3 Combine like terms: -72 + 3 = -69 -69 + 8x + 4x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -69 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.25 + 2x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + 2x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + 2x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + 2x + x2 = 0 + 17.25 2x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 2x + x2 = 17.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 17.25 + 1 Reorder the terms: 1 + 2x + x2 = 17.25 + 1 Combine like terms: 17.25 + 1 = 18.25 1 + 2x + x2 = 18.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 1) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 1 = 4.272001873 Simplifying x + 1 = 4.272001873 Reorder the terms: 1 + x = 4.272001873 Solving 1 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.272001873 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.272001873 + -1 x = 4.272001873 + -1 Combine like terms: 4.272001873 + -1 = 3.272001873 x = 3.272001873 Simplifying x = 3.272001873Subproblem 2
x + 1 = -4.272001873 Simplifying x + 1 = -4.272001873 Reorder the terms: 1 + x = -4.272001873 Solving 1 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.272001873 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.272001873 + -1 x = -4.272001873 + -1 Combine like terms: -4.272001873 + -1 = -5.272001873 x = -5.272001873 Simplifying x = -5.272001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.272001873, -5.272001873}
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