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Simplifying x(2x + -3) = 234 Reorder the terms: x(-3 + 2x) = 234 (-3 * x + 2x * x) = 234 (-3x + 2x2) = 234 Solving -3x + 2x2 = 234 Solving for variable 'x'. Reorder the terms: -234 + -3x + 2x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -234 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -117 + -1.5x + x2 = 0 Move the constant term to the right: Add '117' to each side of the equation. -117 + -1.5x + 117 + x2 = 0 + 117 Reorder the terms: -117 + 117 + -1.5x + x2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + -1.5x + x2 = 0 + 117 -1.5x + x2 = 0 + 117 Combine like terms: 0 + 117 = 117 -1.5x + x2 = 117 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 = 117 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 117 + 0.5625 Combine like terms: 117 + 0.5625 = 117.5625 0.5625 + -1.5x + x2 = 117.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 117.5625 Calculate the square root of the right side: 10.842624221 Break this problem into two subproblems by setting (x + -0.75) equal to 10.842624221 and -10.842624221.Subproblem 1
x + -0.75 = 10.842624221 Simplifying x + -0.75 = 10.842624221 Reorder the terms: -0.75 + x = 10.842624221 Solving -0.75 + x = 10.842624221 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 = 10.842624221 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 10.842624221 + 0.75 x = 10.842624221 + 0.75 Combine like terms: 10.842624221 + 0.75 = 11.592624221 x = 11.592624221 Simplifying x = 11.592624221Subproblem 2
x + -0.75 = -10.842624221 Simplifying x + -0.75 = -10.842624221 Reorder the terms: -0.75 + x = -10.842624221 Solving -0.75 + x = -10.842624221 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 = -10.842624221 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -10.842624221 + 0.75 x = -10.842624221 + 0.75 Combine like terms: -10.842624221 + 0.75 = -10.092624221 x = -10.092624221 Simplifying x = -10.092624221Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.592624221, -10.092624221}
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