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Simplifying 2x2 + 7x + 3 = 30 Reorder the terms: 3 + 7x + 2x2 = 30 Solving 3 + 7x + 2x2 = 30 Solving for variable 'x'. Reorder the terms: 3 + -30 + 7x + 2x2 = 30 + -30 Combine like terms: 3 + -30 = -27 -27 + 7x + 2x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -27 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 3.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 3.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 3.5x + x2 = 0 + 13.5 3.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 3.5x + x2 = 13.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 13.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 13.5 + 3.0625 Combine like terms: 13.5 + 3.0625 = 16.5625 3.0625 + 3.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + 1.75) equal to 4.069705149 and -4.069705149.Subproblem 1
x + 1.75 = 4.069705149 Simplifying x + 1.75 = 4.069705149 Reorder the terms: 1.75 + x = 4.069705149 Solving 1.75 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.069705149 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.069705149 + -1.75 x = 4.069705149 + -1.75 Combine like terms: 4.069705149 + -1.75 = 2.319705149 x = 2.319705149 Simplifying x = 2.319705149Subproblem 2
x + 1.75 = -4.069705149 Simplifying x + 1.75 = -4.069705149 Reorder the terms: 1.75 + x = -4.069705149 Solving 1.75 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.069705149 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.069705149 + -1.75 x = -4.069705149 + -1.75 Combine like terms: -4.069705149 + -1.75 = -5.819705149 x = -5.819705149 Simplifying x = -5.819705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.319705149, -5.819705149}
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