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Simplifying 2x(2x + -3) = 6 + x Reorder the terms: 2x(-3 + 2x) = 6 + x (-3 * 2x + 2x * 2x) = 6 + x (-6x + 4x2) = 6 + x Solving -6x + 4x2 = 6 + x Solving for variable 'x'. Reorder the terms: -6 + -6x + -1x + 4x2 = 6 + x + -6 + -1x Combine like terms: -6x + -1x = -7x -6 + -7x + 4x2 = 6 + x + -6 + -1x Reorder the terms: -6 + -7x + 4x2 = 6 + -6 + x + -1x Combine like terms: 6 + -6 = 0 -6 + -7x + 4x2 = 0 + x + -1x -6 + -7x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -6 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -1.75x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1.75x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1.75x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.75x + x2 = 0 + 1.5 -1.75x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1.75x + x2 = 1.5 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 1.5 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 1.5 + 0.765625 Combine like terms: 1.5 + 0.765625 = 2.265625 0.765625 + -1.75x + x2 = 2.265625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + -0.875) equal to 1.505199322 and -1.505199322.Subproblem 1
x + -0.875 = 1.505199322 Simplifying x + -0.875 = 1.505199322 Reorder the terms: -0.875 + x = 1.505199322 Solving -0.875 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.505199322 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.505199322 + 0.875 x = 1.505199322 + 0.875 Combine like terms: 1.505199322 + 0.875 = 2.380199322 x = 2.380199322 Simplifying x = 2.380199322Subproblem 2
x + -0.875 = -1.505199322 Simplifying x + -0.875 = -1.505199322 Reorder the terms: -0.875 + x = -1.505199322 Solving -0.875 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.505199322 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.505199322 + 0.875 x = -1.505199322 + 0.875 Combine like terms: -1.505199322 + 0.875 = -0.630199322 x = -0.630199322 Simplifying x = -0.630199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.380199322, -0.630199322}
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