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Simplifying 2x2 + -3x = 133 Reorder the terms: -3x + 2x2 = 133 Solving -3x + 2x2 = 133 Solving for variable 'x'. Reorder the terms: -133 + -3x + 2x2 = 133 + -133 Combine like terms: 133 + -133 = 0 -133 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -66.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '66.5' to each side of the equation. -66.5 + -1.5x + 66.5 + x2 = 0 + 66.5 Reorder the terms: -66.5 + 66.5 + -1.5x + x2 = 0 + 66.5 Combine like terms: -66.5 + 66.5 = 0.0 0.0 + -1.5x + x2 = 0 + 66.5 -1.5x + x2 = 0 + 66.5 Combine like terms: 0 + 66.5 = 66.5 -1.5x + x2 = 66.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 66.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 66.5 + 0.5625 Combine like terms: 66.5 + 0.5625 = 67.0625 0.5625 + -1.5x + x2 = 67.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 67.0625 Calculate the square root of the right side: 8.189169677 Break this problem into two subproblems by setting (x + -0.75) equal to 8.189169677 and -8.189169677.Subproblem 1
x + -0.75 = 8.189169677 Simplifying x + -0.75 = 8.189169677 Reorder the terms: -0.75 + x = 8.189169677 Solving -0.75 + x = 8.189169677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 8.189169677 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 8.189169677 + 0.75 x = 8.189169677 + 0.75 Combine like terms: 8.189169677 + 0.75 = 8.939169677 x = 8.939169677 Simplifying x = 8.939169677Subproblem 2
x + -0.75 = -8.189169677 Simplifying x + -0.75 = -8.189169677 Reorder the terms: -0.75 + x = -8.189169677 Solving -0.75 + x = -8.189169677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -8.189169677 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -8.189169677 + 0.75 x = -8.189169677 + 0.75 Combine like terms: -8.189169677 + 0.75 = -7.439169677 x = -7.439169677 Simplifying x = -7.439169677Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.939169677, -7.439169677}
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