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Simplifying 45 = (7x2) + 21x Reorder the terms: 45 = 21x + (7x2) Solving 45 = 21x + (7x2) Solving for variable 'x'. Reorder the terms: 45 + -21x + (-7x2) = 21x + -21x + (7x2) + (-7x2) Combine like terms: 21x + -21x = 0 45 + -21x + (-7x2) = 0 + (7x2) + (-7x2) 45 + -21x + (-7x2) = (7x2) + (-7x2) Combine like terms: (7x2) + (-7x2) = 0 45 + -21x + (-7x2) = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -6.428571429 + 3x + x2 = 0 Move the constant term to the right: Add '6.428571429' to each side of the equation. -6.428571429 + 3x + 6.428571429 + x2 = 0 + 6.428571429 Reorder the terms: -6.428571429 + 6.428571429 + 3x + x2 = 0 + 6.428571429 Combine like terms: -6.428571429 + 6.428571429 = 0.000000000 0.000000000 + 3x + x2 = 0 + 6.428571429 3x + x2 = 0 + 6.428571429 Combine like terms: 0 + 6.428571429 = 6.428571429 3x + x2 = 6.428571429 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 = 6.428571429 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 6.428571429 + 2.25 Combine like terms: 6.428571429 + 2.25 = 8.678571429 2.25 + 3x + x2 = 8.678571429 Factor a perfect square on the left side: ((x) + 1.5)((x) + 1.5) = 8.678571429 Calculate the square root of the right side: 2.945941518 Break this problem into two subproblems by setting ((x) + 1.5) equal to 2.945941518 and -2.945941518.Subproblem 1
(x) + 1.5 = 2.945941518 Simplifying (x) + 1.5 = 2.945941518 x + 1.5 = 2.945941518 Reorder the terms: 1.5 + x = 2.945941518 Solving 1.5 + x = 2.945941518 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 = 2.945941518 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.945941518 + -1.5 x = 2.945941518 + -1.5 Combine like terms: 2.945941518 + -1.5 = 1.445941518 x = 1.445941518 Simplifying x = 1.445941518Subproblem 2
(x) + 1.5 = -2.945941518 Simplifying (x) + 1.5 = -2.945941518 x + 1.5 = -2.945941518 Reorder the terms: 1.5 + x = -2.945941518 Solving 1.5 + x = -2.945941518 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 = -2.945941518 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.945941518 + -1.5 x = -2.945941518 + -1.5 Combine like terms: -2.945941518 + -1.5 = -4.445941518 x = -4.445941518 Simplifying x = -4.445941518Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.445941518, -4.445941518}
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