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Simplifying 3x2 + 6x + 2 = 75 Reorder the terms: 2 + 6x + 3x2 = 75 Solving 2 + 6x + 3x2 = 75 Solving for variable 'x'. Reorder the terms: 2 + -75 + 6x + 3x2 = 75 + -75 Combine like terms: 2 + -75 = -73 -73 + 6x + 3x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -73 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -24.33333333 + 2x + x2 = 0 Move the constant term to the right: Add '24.33333333' to each side of the equation. -24.33333333 + 2x + 24.33333333 + x2 = 0 + 24.33333333 Reorder the terms: -24.33333333 + 24.33333333 + 2x + x2 = 0 + 24.33333333 Combine like terms: -24.33333333 + 24.33333333 = 0.00000000 0.00000000 + 2x + x2 = 0 + 24.33333333 2x + x2 = 0 + 24.33333333 Combine like terms: 0 + 24.33333333 = 24.33333333 2x + x2 = 24.33333333 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 = 24.33333333 + 1 Reorder the terms: 1 + 2x + x2 = 24.33333333 + 1 Combine like terms: 24.33333333 + 1 = 25.33333333 1 + 2x + x2 = 25.33333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 25.33333333 Calculate the square root of the right side: 5.033222957 Break this problem into two subproblems by setting (x + 1) equal to 5.033222957 and -5.033222957.Subproblem 1
x + 1 = 5.033222957 Simplifying x + 1 = 5.033222957 Reorder the terms: 1 + x = 5.033222957 Solving 1 + x = 5.033222957 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 = 5.033222957 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.033222957 + -1 x = 5.033222957 + -1 Combine like terms: 5.033222957 + -1 = 4.033222957 x = 4.033222957 Simplifying x = 4.033222957Subproblem 2
x + 1 = -5.033222957 Simplifying x + 1 = -5.033222957 Reorder the terms: 1 + x = -5.033222957 Solving 1 + x = -5.033222957 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 = -5.033222957 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.033222957 + -1 x = -5.033222957 + -1 Combine like terms: -5.033222957 + -1 = -6.033222957 x = -6.033222957 Simplifying x = -6.033222957Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.033222957, -6.033222957}
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