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Simplifying x2 + -7x = 153 Reorder the terms: -7x + x2 = 153 Solving -7x + x2 = 153 Solving for variable 'x'. Reorder the terms: -153 + -7x + x2 = 153 + -153 Combine like terms: 153 + -153 = 0 -153 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '153' to each side of the equation. -153 + -7x + 153 + x2 = 0 + 153 Reorder the terms: -153 + 153 + -7x + x2 = 0 + 153 Combine like terms: -153 + 153 = 0 0 + -7x + x2 = 0 + 153 -7x + x2 = 0 + 153 Combine like terms: 0 + 153 = 153 -7x + x2 = 153 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 = 153 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 153 + 12.25 Combine like terms: 153 + 12.25 = 165.25 12.25 + -7x + x2 = 165.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 165.25 Calculate the square root of the right side: 12.854960132 Break this problem into two subproblems by setting (x + -3.5) equal to 12.854960132 and -12.854960132.Subproblem 1
x + -3.5 = 12.854960132 Simplifying x + -3.5 = 12.854960132 Reorder the terms: -3.5 + x = 12.854960132 Solving -3.5 + x = 12.854960132 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 = 12.854960132 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 12.854960132 + 3.5 x = 12.854960132 + 3.5 Combine like terms: 12.854960132 + 3.5 = 16.354960132 x = 16.354960132 Simplifying x = 16.354960132Subproblem 2
x + -3.5 = -12.854960132 Simplifying x + -3.5 = -12.854960132 Reorder the terms: -3.5 + x = -12.854960132 Solving -3.5 + x = -12.854960132 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 = -12.854960132 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -12.854960132 + 3.5 x = -12.854960132 + 3.5 Combine like terms: -12.854960132 + 3.5 = -9.354960132 x = -9.354960132 Simplifying x = -9.354960132Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.354960132, -9.354960132}
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