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Simplifying 2x2 + 14x + 49 = 30 Reorder the terms: 49 + 14x + 2x2 = 30 Solving 49 + 14x + 2x2 = 30 Solving for variable 'x'. Reorder the terms: 49 + -30 + 14x + 2x2 = 30 + -30 Combine like terms: 49 + -30 = 19 19 + 14x + 2x2 = 30 + -30 Combine like terms: 30 + -30 = 0 19 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9.5 + 7x + x2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + 7x + -9.5 + x2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + 7x + x2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + 7x + x2 = 0 + -9.5 7x + x2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 7x + x2 = -9.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -9.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -9.5 + 12.25 Combine like terms: -9.5 + 12.25 = 2.75 12.25 + 7x + x2 = 2.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + 3.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + 3.5 = 1.658312395 Simplifying x + 3.5 = 1.658312395 Reorder the terms: 3.5 + x = 1.658312395 Solving 3.5 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 1.658312395 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.658312395 + -3.5 x = 1.658312395 + -3.5 Combine like terms: 1.658312395 + -3.5 = -1.841687605 x = -1.841687605 Simplifying x = -1.841687605Subproblem 2
x + 3.5 = -1.658312395 Simplifying x + 3.5 = -1.658312395 Reorder the terms: 3.5 + x = -1.658312395 Solving 3.5 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -1.658312395 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.658312395 + -3.5 x = -1.658312395 + -3.5 Combine like terms: -1.658312395 + -3.5 = -5.158312395 x = -5.158312395 Simplifying x = -5.158312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.841687605, -5.158312395}
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