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Simplifying 2x2 + -15x = 1 Reorder the terms: -15x + 2x2 = 1 Solving -15x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -15x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -7.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -7.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -7.5x + x2 = 0 + 0.5 -7.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -7.5x + x2 = 0.5 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 = 0.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 0.5 + 14.0625 Combine like terms: 0.5 + 14.0625 = 14.5625 14.0625 + -7.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + -3.75) equal to 3.816084381 and -3.816084381.Subproblem 1
x + -3.75 = 3.816084381 Simplifying x + -3.75 = 3.816084381 Reorder the terms: -3.75 + x = 3.816084381 Solving -3.75 + x = 3.816084381 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 = 3.816084381 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.816084381 + 3.75 x = 3.816084381 + 3.75 Combine like terms: 3.816084381 + 3.75 = 7.566084381 x = 7.566084381 Simplifying x = 7.566084381Subproblem 2
x + -3.75 = -3.816084381 Simplifying x + -3.75 = -3.816084381 Reorder the terms: -3.75 + x = -3.816084381 Solving -3.75 + x = -3.816084381 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 = -3.816084381 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.816084381 + 3.75 x = -3.816084381 + 3.75 Combine like terms: -3.816084381 + 3.75 = -0.066084381 x = -0.066084381 Simplifying x = -0.066084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.566084381, -0.066084381}
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