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Simplifying 2x2 + 18x + -7 = 0 Reorder the terms: -7 + 18x + 2x2 = 0 Solving -7 + 18x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 9x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 9x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 9x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 9x + x2 = 0 + 3.5 9x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 9x + x2 = 3.5 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 3.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 3.5 + 20.25 Combine like terms: 3.5 + 20.25 = 23.75 20.25 + 9x + x2 = 23.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 23.75 Calculate the square root of the right side: 4.873397172 Break this problem into two subproblems by setting (x + 4.5) equal to 4.873397172 and -4.873397172.Subproblem 1
x + 4.5 = 4.873397172 Simplifying x + 4.5 = 4.873397172 Reorder the terms: 4.5 + x = 4.873397172 Solving 4.5 + x = 4.873397172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.873397172 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.873397172 + -4.5 x = 4.873397172 + -4.5 Combine like terms: 4.873397172 + -4.5 = 0.373397172 x = 0.373397172 Simplifying x = 0.373397172Subproblem 2
x + 4.5 = -4.873397172 Simplifying x + 4.5 = -4.873397172 Reorder the terms: 4.5 + x = -4.873397172 Solving 4.5 + x = -4.873397172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.873397172 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.873397172 + -4.5 x = -4.873397172 + -4.5 Combine like terms: -4.873397172 + -4.5 = -9.373397172 x = -9.373397172 Simplifying x = -9.373397172Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.373397172, -9.373397172}
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