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Simplifying x2 = -15x + 12 Reorder the terms: x2 = 12 + -15x Solving x2 = 12 + -15x Solving for variable 'x'. Reorder the terms: -12 + 15x + x2 = 12 + -15x + -12 + 15x Reorder the terms: -12 + 15x + x2 = 12 + -12 + -15x + 15x Combine like terms: 12 + -12 = 0 -12 + 15x + x2 = 0 + -15x + 15x -12 + 15x + x2 = -15x + 15x Combine like terms: -15x + 15x = 0 -12 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 15x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 15x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 15x + x2 = 0 + 12 15x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 15x + x2 = 12 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 = 12 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 12 + 56.25 Combine like terms: 12 + 56.25 = 68.25 56.25 + 15x + x2 = 68.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 7.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + 7.5 = 8.261355821 Simplifying x + 7.5 = 8.261355821 Reorder the terms: 7.5 + x = 8.261355821 Solving 7.5 + x = 8.261355821 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 = 8.261355821 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.261355821 + -7.5 x = 8.261355821 + -7.5 Combine like terms: 8.261355821 + -7.5 = 0.761355821 x = 0.761355821 Simplifying x = 0.761355821Subproblem 2
x + 7.5 = -8.261355821 Simplifying x + 7.5 = -8.261355821 Reorder the terms: 7.5 + x = -8.261355821 Solving 7.5 + x = -8.261355821 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 = -8.261355821 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.261355821 + -7.5 x = -8.261355821 + -7.5 Combine like terms: -8.261355821 + -7.5 = -15.761355821 x = -15.761355821 Simplifying x = -15.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.761355821, -15.761355821}
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