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Simplifying x2 + 12x = 360 Reorder the terms: 12x + x2 = 360 Solving 12x + x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 12x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 12x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 12x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 12x + x2 = 0 + 360 12x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 12x + x2 = 360 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 360 + 36 Reorder the terms: 36 + 12x + x2 = 360 + 36 Combine like terms: 360 + 36 = 396 36 + 12x + x2 = 396 Factor a perfect square on the left side: (x + 6)(x + 6) = 396 Calculate the square root of the right side: 19.899748742 Break this problem into two subproblems by setting (x + 6) equal to 19.899748742 and -19.899748742.Subproblem 1
x + 6 = 19.899748742 Simplifying x + 6 = 19.899748742 Reorder the terms: 6 + x = 19.899748742 Solving 6 + x = 19.899748742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 19.899748742 + -6 Combine like terms: 6 + -6 = 0 0 + x = 19.899748742 + -6 x = 19.899748742 + -6 Combine like terms: 19.899748742 + -6 = 13.899748742 x = 13.899748742 Simplifying x = 13.899748742Subproblem 2
x + 6 = -19.899748742 Simplifying x + 6 = -19.899748742 Reorder the terms: 6 + x = -19.899748742 Solving 6 + x = -19.899748742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -19.899748742 + -6 Combine like terms: 6 + -6 = 0 0 + x = -19.899748742 + -6 x = -19.899748742 + -6 Combine like terms: -19.899748742 + -6 = -25.899748742 x = -25.899748742 Simplifying x = -25.899748742Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.899748742, -25.899748742}
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