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Simplifying x(x + -7) = 31 Reorder the terms: x(-7 + x) = 31 (-7 * x + x * x) = 31 (-7x + x2) = 31 Solving -7x + x2 = 31 Solving for variable 'x'. Reorder the terms: -31 + -7x + x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -7x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -7x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -7x + x2 = 0 + 31 -7x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -7x + x2 = 31 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 = 31 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 31 + 12.25 Combine like terms: 31 + 12.25 = 43.25 12.25 + -7x + x2 = 43.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + -3.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + -3.5 = 6.576473219 Simplifying x + -3.5 = 6.576473219 Reorder the terms: -3.5 + x = 6.576473219 Solving -3.5 + x = 6.576473219 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 = 6.576473219 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.576473219 + 3.5 x = 6.576473219 + 3.5 Combine like terms: 6.576473219 + 3.5 = 10.076473219 x = 10.076473219 Simplifying x = 10.076473219Subproblem 2
x + -3.5 = -6.576473219 Simplifying x + -3.5 = -6.576473219 Reorder the terms: -3.5 + x = -6.576473219 Solving -3.5 + x = -6.576473219 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 = -6.576473219 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.576473219 + 3.5 x = -6.576473219 + 3.5 Combine like terms: -6.576473219 + 3.5 = -3.076473219 x = -3.076473219 Simplifying x = -3.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.076473219, -3.076473219}
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