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Simplifying 2x2 + 8x + -3 = 24 Reorder the terms: -3 + 8x + 2x2 = 24 Solving -3 + 8x + 2x2 = 24 Solving for variable 'x'. Reorder the terms: -3 + -24 + 8x + 2x2 = 24 + -24 Combine like terms: -3 + -24 = -27 -27 + 8x + 2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -27 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 4x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 4x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 4x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 4x + x2 = 0 + 13.5 4x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 4x + x2 = 13.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 13.5 + 4 Reorder the terms: 4 + 4x + x2 = 13.5 + 4 Combine like terms: 13.5 + 4 = 17.5 4 + 4x + x2 = 17.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 17.5 Calculate the square root of the right side: 4.183300133 Break this problem into two subproblems by setting (x + 2) equal to 4.183300133 and -4.183300133.Subproblem 1
x + 2 = 4.183300133 Simplifying x + 2 = 4.183300133 Reorder the terms: 2 + x = 4.183300133 Solving 2 + x = 4.183300133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.183300133 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.183300133 + -2 x = 4.183300133 + -2 Combine like terms: 4.183300133 + -2 = 2.183300133 x = 2.183300133 Simplifying x = 2.183300133Subproblem 2
x + 2 = -4.183300133 Simplifying x + 2 = -4.183300133 Reorder the terms: 2 + x = -4.183300133 Solving 2 + x = -4.183300133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.183300133 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.183300133 + -2 x = -4.183300133 + -2 Combine like terms: -4.183300133 + -2 = -6.183300133 x = -6.183300133 Simplifying x = -6.183300133Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.183300133, -6.183300133}
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