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Simplifying 2x2 + -12 = 15x Reorder the terms: -12 + 2x2 = 15x Solving -12 + 2x2 = 15x Solving for variable 'x'. Reorder the terms: -12 + -15x + 2x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -12 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -7.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -7.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -7.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7.5x + x2 = 0 + 6 -7.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -7.5x + x2 = 6 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 6 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 6 + 14.0625 Combine like terms: 6 + 14.0625 = 20.0625 14.0625 + -7.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + -3.75) equal to 4.479118217 and -4.479118217.Subproblem 1
x + -3.75 = 4.479118217 Simplifying x + -3.75 = 4.479118217 Reorder the terms: -3.75 + x = 4.479118217 Solving -3.75 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 4.479118217 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.479118217 + 3.75 x = 4.479118217 + 3.75 Combine like terms: 4.479118217 + 3.75 = 8.229118217 x = 8.229118217 Simplifying x = 8.229118217Subproblem 2
x + -3.75 = -4.479118217 Simplifying x + -3.75 = -4.479118217 Reorder the terms: -3.75 + x = -4.479118217 Solving -3.75 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -4.479118217 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.479118217 + 3.75 x = -4.479118217 + 3.75 Combine like terms: -4.479118217 + 3.75 = -0.729118217 x = -0.729118217 Simplifying x = -0.729118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.229118217, -0.729118217}
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