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Simplifying -7x2 + -21x + 40 = 0 Reorder the terms: 40 + -21x + -7x2 = 0 Solving 40 + -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'. -5.714285714 + 3x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + 3x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + 3x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + 3x + x2 = 0 + 5.714285714 3x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 3x + x2 = 5.714285714 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 = 5.714285714 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 5.714285714 + 2.25 Combine like terms: 5.714285714 + 2.25 = 7.964285714 2.25 + 3x + x2 = 7.964285714 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 7.964285714 Calculate the square root of the right side: 2.822106609 Break this problem into two subproblems by setting (x + 1.5) equal to 2.822106609 and -2.822106609.Subproblem 1
x + 1.5 = 2.822106609 Simplifying x + 1.5 = 2.822106609 Reorder the terms: 1.5 + x = 2.822106609 Solving 1.5 + x = 2.822106609 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 = 2.822106609 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.822106609 + -1.5 x = 2.822106609 + -1.5 Combine like terms: 2.822106609 + -1.5 = 1.322106609 x = 1.322106609 Simplifying x = 1.322106609Subproblem 2
x + 1.5 = -2.822106609 Simplifying x + 1.5 = -2.822106609 Reorder the terms: 1.5 + x = -2.822106609 Solving 1.5 + x = -2.822106609 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 = -2.822106609 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.822106609 + -1.5 x = -2.822106609 + -1.5 Combine like terms: -2.822106609 + -1.5 = -4.322106609 x = -4.322106609 Simplifying x = -4.322106609Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.322106609, -4.322106609}
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