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Simplifying x2 + 7x + -152 = 0 Reorder the terms: -152 + 7x + x2 = 0 Solving -152 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '152' to each side of the equation. -152 + 7x + 152 + x2 = 0 + 152 Reorder the terms: -152 + 152 + 7x + x2 = 0 + 152 Combine like terms: -152 + 152 = 0 0 + 7x + x2 = 0 + 152 7x + x2 = 0 + 152 Combine like terms: 0 + 152 = 152 7x + x2 = 152 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 = 152 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 152 + 12.25 Combine like terms: 152 + 12.25 = 164.25 12.25 + 7x + x2 = 164.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 164.25 Calculate the square root of the right side: 12.816005618 Break this problem into two subproblems by setting (x + 3.5) equal to 12.816005618 and -12.816005618.Subproblem 1
x + 3.5 = 12.816005618 Simplifying x + 3.5 = 12.816005618 Reorder the terms: 3.5 + x = 12.816005618 Solving 3.5 + x = 12.816005618 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 = 12.816005618 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 12.816005618 + -3.5 x = 12.816005618 + -3.5 Combine like terms: 12.816005618 + -3.5 = 9.316005618 x = 9.316005618 Simplifying x = 9.316005618Subproblem 2
x + 3.5 = -12.816005618 Simplifying x + 3.5 = -12.816005618 Reorder the terms: 3.5 + x = -12.816005618 Solving 3.5 + x = -12.816005618 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 = -12.816005618 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -12.816005618 + -3.5 x = -12.816005618 + -3.5 Combine like terms: -12.816005618 + -3.5 = -16.316005618 x = -16.316005618 Simplifying x = -16.316005618Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.316005618, -16.316005618}
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