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Simplifying 2x2 + 4x + -95 = 0 Reorder the terms: -95 + 4x + 2x2 = 0 Solving -95 + 4x + 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'. -47.5 + 2x + x2 = 0 Move the constant term to the right: Add '47.5' to each side of the equation. -47.5 + 2x + 47.5 + x2 = 0 + 47.5 Reorder the terms: -47.5 + 47.5 + 2x + x2 = 0 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + 2x + x2 = 0 + 47.5 2x + x2 = 0 + 47.5 Combine like terms: 0 + 47.5 = 47.5 2x + x2 = 47.5 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 = 47.5 + 1 Reorder the terms: 1 + 2x + x2 = 47.5 + 1 Combine like terms: 47.5 + 1 = 48.5 1 + 2x + x2 = 48.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 48.5 Calculate the square root of the right side: 6.964194139 Break this problem into two subproblems by setting (x + 1) equal to 6.964194139 and -6.964194139.Subproblem 1
x + 1 = 6.964194139 Simplifying x + 1 = 6.964194139 Reorder the terms: 1 + x = 6.964194139 Solving 1 + x = 6.964194139 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 = 6.964194139 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.964194139 + -1 x = 6.964194139 + -1 Combine like terms: 6.964194139 + -1 = 5.964194139 x = 5.964194139 Simplifying x = 5.964194139Subproblem 2
x + 1 = -6.964194139 Simplifying x + 1 = -6.964194139 Reorder the terms: 1 + x = -6.964194139 Solving 1 + x = -6.964194139 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 = -6.964194139 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.964194139 + -1 x = -6.964194139 + -1 Combine like terms: -6.964194139 + -1 = -7.964194139 x = -7.964194139 Simplifying x = -7.964194139Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.964194139, -7.964194139}
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