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Simplifying -7x2 + -4x + 629 = 0 Reorder the terms: 629 + -4x + -7x2 = 0 Solving 629 + -4x + -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'. -89.85714286 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '89.85714286' to each side of the equation. -89.85714286 + 0.5714285714x + 89.85714286 + x2 = 0 + 89.85714286 Reorder the terms: -89.85714286 + 89.85714286 + 0.5714285714x + x2 = 0 + 89.85714286 Combine like terms: -89.85714286 + 89.85714286 = 0.00000000 0.00000000 + 0.5714285714x + x2 = 0 + 89.85714286 0.5714285714x + x2 = 0 + 89.85714286 Combine like terms: 0 + 89.85714286 = 89.85714286 0.5714285714x + x2 = 89.85714286 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 89.85714286 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 89.85714286 + 0.08163265305 Combine like terms: 89.85714286 + 0.08163265305 = 89.93877551305 0.08163265305 + 0.5714285714x + x2 = 89.93877551305 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 89.93877551305 Calculate the square root of the right side: 9.483605618 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 9.483605618 and -9.483605618.Subproblem 1
x + 0.2857142857 = 9.483605618 Simplifying x + 0.2857142857 = 9.483605618 Reorder the terms: 0.2857142857 + x = 9.483605618 Solving 0.2857142857 + x = 9.483605618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 9.483605618 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 9.483605618 + -0.2857142857 x = 9.483605618 + -0.2857142857 Combine like terms: 9.483605618 + -0.2857142857 = 9.1978913323 x = 9.1978913323 Simplifying x = 9.1978913323Subproblem 2
x + 0.2857142857 = -9.483605618 Simplifying x + 0.2857142857 = -9.483605618 Reorder the terms: 0.2857142857 + x = -9.483605618 Solving 0.2857142857 + x = -9.483605618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -9.483605618 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -9.483605618 + -0.2857142857 x = -9.483605618 + -0.2857142857 Combine like terms: -9.483605618 + -0.2857142857 = -9.7693199037 x = -9.7693199037 Simplifying x = -9.7693199037Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.1978913323, -9.7693199037}
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