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Simplifying 7x2 + 7x + -295 = 0 Reorder the terms: -295 + 7x + 7x2 = 0 Solving -295 + 7x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -42.14285714 + x + x2 = 0 Move the constant term to the right: Add '42.14285714' to each side of the equation. -42.14285714 + x + 42.14285714 + x2 = 0 + 42.14285714 Reorder the terms: -42.14285714 + 42.14285714 + x + x2 = 0 + 42.14285714 Combine like terms: -42.14285714 + 42.14285714 = 0.00000000 0.00000000 + x + x2 = 0 + 42.14285714 x + x2 = 0 + 42.14285714 Combine like terms: 0 + 42.14285714 = 42.14285714 x + x2 = 42.14285714 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 42.14285714 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 42.14285714 + 0.25 Combine like terms: 42.14285714 + 0.25 = 42.39285714 1.25 + x2 = 42.39285714 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 42.39285714 Calculate the square root of the right side: 6.510979737 Break this problem into two subproblems by setting (x + 0.5) equal to 6.510979737 and -6.510979737.Subproblem 1
x + 0.5 = 6.510979737 Simplifying x + 0.5 = 6.510979737 Reorder the terms: 0.5 + x = 6.510979737 Solving 0.5 + x = 6.510979737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.510979737 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.510979737 + -0.5 x = 6.510979737 + -0.5 Combine like terms: 6.510979737 + -0.5 = 6.010979737 x = 6.010979737 Simplifying x = 6.010979737Subproblem 2
x + 0.5 = -6.510979737 Simplifying x + 0.5 = -6.510979737 Reorder the terms: 0.5 + x = -6.510979737 Solving 0.5 + x = -6.510979737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.510979737 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.510979737 + -0.5 x = -6.510979737 + -0.5 Combine like terms: -6.510979737 + -0.5 = -7.010979737 x = -7.010979737 Simplifying x = -7.010979737Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.010979737, -7.010979737}
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