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Simplifying x2 + 7x + -147 = 0 Reorder the terms: -147 + 7x + x2 = 0 Solving -147 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + 7x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + 7x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + 7x + x2 = 0 + 147 7x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 7x + x2 = 147 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 = 147 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 147 + 12.25 Combine like terms: 147 + 12.25 = 159.25 12.25 + 7x + x2 = 159.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 159.25 Calculate the square root of the right side: 12.619429464 Break this problem into two subproblems by setting (x + 3.5) equal to 12.619429464 and -12.619429464.Subproblem 1
x + 3.5 = 12.619429464 Simplifying x + 3.5 = 12.619429464 Reorder the terms: 3.5 + x = 12.619429464 Solving 3.5 + x = 12.619429464 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 = 12.619429464 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 12.619429464 + -3.5 x = 12.619429464 + -3.5 Combine like terms: 12.619429464 + -3.5 = 9.119429464 x = 9.119429464 Simplifying x = 9.119429464Subproblem 2
x + 3.5 = -12.619429464 Simplifying x + 3.5 = -12.619429464 Reorder the terms: 3.5 + x = -12.619429464 Solving 3.5 + x = -12.619429464 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 = -12.619429464 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -12.619429464 + -3.5 x = -12.619429464 + -3.5 Combine like terms: -12.619429464 + -3.5 = -16.119429464 x = -16.119429464 Simplifying x = -16.119429464Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.119429464, -16.119429464}
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