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Simplifying 7x2 + -7x + -297 = 0 Reorder the terms: -297 + -7x + 7x2 = 0 Solving -297 + -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'. -42.42857143 + -1x + x2 = 0 Move the constant term to the right: Add '42.42857143' to each side of the equation. -42.42857143 + -1x + 42.42857143 + x2 = 0 + 42.42857143 Reorder the terms: -42.42857143 + 42.42857143 + -1x + x2 = 0 + 42.42857143 Combine like terms: -42.42857143 + 42.42857143 = 0.00000000 0.00000000 + -1x + x2 = 0 + 42.42857143 -1x + x2 = 0 + 42.42857143 Combine like terms: 0 + 42.42857143 = 42.42857143 -1x + x2 = 42.42857143 The x term is -1x. 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. -1x + 0.25 + x2 = 42.42857143 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 42.42857143 + 0.25 Combine like terms: 42.42857143 + 0.25 = 42.67857143 0.25 + -1x + x2 = 42.67857143 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 42.67857143 Calculate the square root of the right side: 6.532883852 Break this problem into two subproblems by setting (x + -0.5) equal to 6.532883852 and -6.532883852.Subproblem 1
x + -0.5 = 6.532883852 Simplifying x + -0.5 = 6.532883852 Reorder the terms: -0.5 + x = 6.532883852 Solving -0.5 + x = 6.532883852 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 = 6.532883852 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.532883852 + 0.5 x = 6.532883852 + 0.5 Combine like terms: 6.532883852 + 0.5 = 7.032883852 x = 7.032883852 Simplifying x = 7.032883852Subproblem 2
x + -0.5 = -6.532883852 Simplifying x + -0.5 = -6.532883852 Reorder the terms: -0.5 + x = -6.532883852 Solving -0.5 + x = -6.532883852 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 = -6.532883852 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.532883852 + 0.5 x = -6.532883852 + 0.5 Combine like terms: -6.532883852 + 0.5 = -6.032883852 x = -6.032883852 Simplifying x = -6.032883852Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.032883852, -6.032883852}
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