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Simplifying 4x(x + -1.5) = 1 Reorder the terms: 4x(-1.5 + x) = 1 (-1.5 * 4x + x * 4x) = 1 (-6x + 4x2) = 1 Solving -6x + 4x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -6x + 4x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.5x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.5x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.5x + x2 = 0 + 0.25 -1.5x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.5x + x2 = 0.25 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 = 0.25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.25 + 0.5625 Combine like terms: 0.25 + 0.5625 = 0.8125 0.5625 + -1.5x + x2 = 0.8125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (x + -0.75) equal to 0.901387819 and -0.901387819.Subproblem 1
x + -0.75 = 0.901387819 Simplifying x + -0.75 = 0.901387819 Reorder the terms: -0.75 + x = 0.901387819 Solving -0.75 + x = 0.901387819 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 = 0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.901387819 + 0.75 x = 0.901387819 + 0.75 Combine like terms: 0.901387819 + 0.75 = 1.651387819 x = 1.651387819 Simplifying x = 1.651387819Subproblem 2
x + -0.75 = -0.901387819 Simplifying x + -0.75 = -0.901387819 Reorder the terms: -0.75 + x = -0.901387819 Solving -0.75 + x = -0.901387819 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 = -0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.901387819 + 0.75 x = -0.901387819 + 0.75 Combine like terms: -0.901387819 + 0.75 = -0.151387819 x = -0.151387819 Simplifying x = -0.151387819Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.651387819, -0.151387819}
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