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Simplifying x2 + 7x + -140 = 0 Reorder the terms: -140 + 7x + x2 = 0 Solving -140 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 7x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 7x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 7x + x2 = 0 + 140 7x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 7x + x2 = 140 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 = 140 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 140 + 12.25 Combine like terms: 140 + 12.25 = 152.25 12.25 + 7x + x2 = 152.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 152.25 Calculate the square root of the right side: 12.338962679 Break this problem into two subproblems by setting (x + 3.5) equal to 12.338962679 and -12.338962679.Subproblem 1
x + 3.5 = 12.338962679 Simplifying x + 3.5 = 12.338962679 Reorder the terms: 3.5 + x = 12.338962679 Solving 3.5 + x = 12.338962679 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 = 12.338962679 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 12.338962679 + -3.5 x = 12.338962679 + -3.5 Combine like terms: 12.338962679 + -3.5 = 8.838962679 x = 8.838962679 Simplifying x = 8.838962679Subproblem 2
x + 3.5 = -12.338962679 Simplifying x + 3.5 = -12.338962679 Reorder the terms: 3.5 + x = -12.338962679 Solving 3.5 + x = -12.338962679 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 = -12.338962679 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -12.338962679 + -3.5 x = -12.338962679 + -3.5 Combine like terms: -12.338962679 + -3.5 = -15.838962679 x = -15.838962679 Simplifying x = -15.838962679Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.838962679, -15.838962679}
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