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Simplifying x2 + 2x + 4x + -15 = 360 Reorder the terms: -15 + 2x + 4x + x2 = 360 Combine like terms: 2x + 4x = 6x -15 + 6x + x2 = 360 Solving -15 + 6x + x2 = 360 Solving for variable 'x'. Reorder the terms: -15 + -360 + 6x + x2 = 360 + -360 Combine like terms: -15 + -360 = -375 -375 + 6x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -375 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '375' to each side of the equation. -375 + 6x + 375 + x2 = 0 + 375 Reorder the terms: -375 + 375 + 6x + x2 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + 6x + x2 = 0 + 375 6x + x2 = 0 + 375 Combine like terms: 0 + 375 = 375 6x + x2 = 375 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 375 + 9 Reorder the terms: 9 + 6x + x2 = 375 + 9 Combine like terms: 375 + 9 = 384 9 + 6x + x2 = 384 Factor a perfect square on the left side: (x + 3)(x + 3) = 384 Calculate the square root of the right side: 19.595917942 Break this problem into two subproblems by setting (x + 3) equal to 19.595917942 and -19.595917942.Subproblem 1
x + 3 = 19.595917942 Simplifying x + 3 = 19.595917942 Reorder the terms: 3 + x = 19.595917942 Solving 3 + x = 19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 19.595917942 + -3 Combine like terms: 3 + -3 = 0 0 + x = 19.595917942 + -3 x = 19.595917942 + -3 Combine like terms: 19.595917942 + -3 = 16.595917942 x = 16.595917942 Simplifying x = 16.595917942Subproblem 2
x + 3 = -19.595917942 Simplifying x + 3 = -19.595917942 Reorder the terms: 3 + x = -19.595917942 Solving 3 + x = -19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -19.595917942 + -3 Combine like terms: 3 + -3 = 0 0 + x = -19.595917942 + -3 x = -19.595917942 + -3 Combine like terms: -19.595917942 + -3 = -22.595917942 x = -22.595917942 Simplifying x = -22.595917942Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.595917942, -22.595917942}
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