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Simplifying 15x + -12 = 2x2 Reorder the terms: -12 + 15x = 2x2 Solving -12 + 15x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 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 = 8.0625 14.0625 + -7.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -3.75) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -3.75 = 2.839454173 Simplifying x + -3.75 = 2.839454173 Reorder the terms: -3.75 + x = 2.839454173 Solving -3.75 + x = 2.839454173 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 = 2.839454173 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 2.839454173 + 3.75 x = 2.839454173 + 3.75 Combine like terms: 2.839454173 + 3.75 = 6.589454173 x = 6.589454173 Simplifying x = 6.589454173Subproblem 2
x + -3.75 = -2.839454173 Simplifying x + -3.75 = -2.839454173 Reorder the terms: -3.75 + x = -2.839454173 Solving -3.75 + x = -2.839454173 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 = -2.839454173 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -2.839454173 + 3.75 x = -2.839454173 + 3.75 Combine like terms: -2.839454173 + 3.75 = 0.910545827 x = 0.910545827 Simplifying x = 0.910545827Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.589454173, 0.910545827}
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