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Simplifying x2 + 15x + -270 = 0 Reorder the terms: -270 + 15x + x2 = 0 Solving -270 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 15x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + 15x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 15x + x2 = 0 + 270 15x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 15x + x2 = 270 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 = 270 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 270 + 56.25 Combine like terms: 270 + 56.25 = 326.25 56.25 + 15x + x2 = 326.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 326.25 Calculate the square root of the right side: 18.062391868 Break this problem into two subproblems by setting (x + 7.5) equal to 18.062391868 and -18.062391868.Subproblem 1
x + 7.5 = 18.062391868 Simplifying x + 7.5 = 18.062391868 Reorder the terms: 7.5 + x = 18.062391868 Solving 7.5 + x = 18.062391868 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 = 18.062391868 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 18.062391868 + -7.5 x = 18.062391868 + -7.5 Combine like terms: 18.062391868 + -7.5 = 10.562391868 x = 10.562391868 Simplifying x = 10.562391868Subproblem 2
x + 7.5 = -18.062391868 Simplifying x + 7.5 = -18.062391868 Reorder the terms: 7.5 + x = -18.062391868 Solving 7.5 + x = -18.062391868 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 = -18.062391868 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -18.062391868 + -7.5 x = -18.062391868 + -7.5 Combine like terms: -18.062391868 + -7.5 = -25.562391868 x = -25.562391868 Simplifying x = -25.562391868Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.562391868, -25.562391868}
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