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Simplifying 2x2 + 14x + 3 = 0 Reorder the terms: 3 + 14x + 2x2 = 0 Solving 3 + 14x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 7x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 7x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 7x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 7x + x2 = 0 + -1.5 7x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 7x + x2 = -1.5 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 = -1.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -1.5 + 12.25 Combine like terms: -1.5 + 12.25 = 10.75 12.25 + 7x + x2 = 10.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x + 3.5) equal to 3.278719262 and -3.278719262.Subproblem 1
x + 3.5 = 3.278719262 Simplifying x + 3.5 = 3.278719262 Reorder the terms: 3.5 + x = 3.278719262 Solving 3.5 + x = 3.278719262 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 = 3.278719262 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.278719262 + -3.5 x = 3.278719262 + -3.5 Combine like terms: 3.278719262 + -3.5 = -0.221280738 x = -0.221280738 Simplifying x = -0.221280738Subproblem 2
x + 3.5 = -3.278719262 Simplifying x + 3.5 = -3.278719262 Reorder the terms: 3.5 + x = -3.278719262 Solving 3.5 + x = -3.278719262 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 = -3.278719262 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.278719262 + -3.5 x = -3.278719262 + -3.5 Combine like terms: -3.278719262 + -3.5 = -6.778719262 x = -6.778719262 Simplifying x = -6.778719262Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.221280738, -6.778719262}
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