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Simplifying x2 + 3x + -21 = 0 Reorder the terms: -21 + 3x + x2 = 0 Solving -21 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 3x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 3x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 3x + x2 = 0 + 21 3x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 3x + x2 = 21 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 = 21 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 21 + 2.25 Combine like terms: 21 + 2.25 = 23.25 2.25 + 3x + x2 = 23.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + 1.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + 1.5 = 4.82182538 Simplifying x + 1.5 = 4.82182538 Reorder the terms: 1.5 + x = 4.82182538 Solving 1.5 + x = 4.82182538 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 = 4.82182538 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.82182538 + -1.5 x = 4.82182538 + -1.5 Combine like terms: 4.82182538 + -1.5 = 3.32182538 x = 3.32182538 Simplifying x = 3.32182538Subproblem 2
x + 1.5 = -4.82182538 Simplifying x + 1.5 = -4.82182538 Reorder the terms: 1.5 + x = -4.82182538 Solving 1.5 + x = -4.82182538 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 = -4.82182538 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.82182538 + -1.5 x = -4.82182538 + -1.5 Combine like terms: -4.82182538 + -1.5 = -6.32182538 x = -6.32182538 Simplifying x = -6.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.32182538, -6.32182538}
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