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Simplifying 6x2 + 1.5x + -13.5 = 0 Reorder the terms: -13.5 + 1.5x + 6x2 = 0 Solving -13.5 + 1.5x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.25x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.25x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.25x + x2 = 0 + 2.25 0.25x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.25x + x2 = 2.25 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 2.25 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 2.25 + 0.015625 Combine like terms: 2.25 + 0.015625 = 2.265625 0.015625 + 0.25x + x2 = 2.265625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + 0.125) equal to 1.505199322 and -1.505199322.Subproblem 1
x + 0.125 = 1.505199322 Simplifying x + 0.125 = 1.505199322 Reorder the terms: 0.125 + x = 1.505199322 Solving 0.125 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.505199322 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.505199322 + -0.125 x = 1.505199322 + -0.125 Combine like terms: 1.505199322 + -0.125 = 1.380199322 x = 1.380199322 Simplifying x = 1.380199322Subproblem 2
x + 0.125 = -1.505199322 Simplifying x + 0.125 = -1.505199322 Reorder the terms: 0.125 + x = -1.505199322 Solving 0.125 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.505199322 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.505199322 + -0.125 x = -1.505199322 + -0.125 Combine like terms: -1.505199322 + -0.125 = -1.630199322 x = -1.630199322 Simplifying x = -1.630199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.380199322, -1.630199322}
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