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Simplifying x2 + 15x + -490 = 0 Reorder the terms: -490 + 15x + x2 = 0 Solving -490 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '490' to each side of the equation. -490 + 15x + 490 + x2 = 0 + 490 Reorder the terms: -490 + 490 + 15x + x2 = 0 + 490 Combine like terms: -490 + 490 = 0 0 + 15x + x2 = 0 + 490 15x + x2 = 0 + 490 Combine like terms: 0 + 490 = 490 15x + x2 = 490 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 490 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 490 + 56.25 Combine like terms: 490 + 56.25 = 546.25 56.25 + 15x + x2 = 546.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 546.25 Calculate the square root of the right side: 23.371991785 Break this problem into two subproblems by setting (x + 7.5) equal to 23.371991785 and -23.371991785.Subproblem 1
x + 7.5 = 23.371991785 Simplifying x + 7.5 = 23.371991785 Reorder the terms: 7.5 + x = 23.371991785 Solving 7.5 + x = 23.371991785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 23.371991785 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 23.371991785 + -7.5 x = 23.371991785 + -7.5 Combine like terms: 23.371991785 + -7.5 = 15.871991785 x = 15.871991785 Simplifying x = 15.871991785Subproblem 2
x + 7.5 = -23.371991785 Simplifying x + 7.5 = -23.371991785 Reorder the terms: 7.5 + x = -23.371991785 Solving 7.5 + x = -23.371991785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -23.371991785 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -23.371991785 + -7.5 x = -23.371991785 + -7.5 Combine like terms: -23.371991785 + -7.5 = -30.871991785 x = -30.871991785 Simplifying x = -30.871991785Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.871991785, -30.871991785}
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