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Simplifying 7x2 + 21x + -18 = 0 Reorder the terms: -18 + 21x + 7x2 = 0 Solving -18 + 21x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + 3x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + 3x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + 3x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + 3x + x2 = 0 + 2.571428571 3x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 3x + x2 = 2.571428571 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2.571428571 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.571428571 + 2.25 Combine like terms: 2.571428571 + 2.25 = 4.821428571 2.25 + 3x + x2 = 4.821428571 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.821428571 Calculate the square root of the right side: 2.195775164 Break this problem into two subproblems by setting (x + 1.5) equal to 2.195775164 and -2.195775164.Subproblem 1
x + 1.5 = 2.195775164 Simplifying x + 1.5 = 2.195775164 Reorder the terms: 1.5 + x = 2.195775164 Solving 1.5 + x = 2.195775164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.195775164 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.195775164 + -1.5 x = 2.195775164 + -1.5 Combine like terms: 2.195775164 + -1.5 = 0.695775164 x = 0.695775164 Simplifying x = 0.695775164Subproblem 2
x + 1.5 = -2.195775164 Simplifying x + 1.5 = -2.195775164 Reorder the terms: 1.5 + x = -2.195775164 Solving 1.5 + x = -2.195775164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.195775164 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.195775164 + -1.5 x = -2.195775164 + -1.5 Combine like terms: -2.195775164 + -1.5 = -3.695775164 x = -3.695775164 Simplifying x = -3.695775164Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.695775164, -3.695775164}
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